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Archaeoastronomy in the Old World
About this book This volume summarises the proceedings of a conference which took place at the University of Oxford in September 1981. Held under the auspices of the International Astronomical Union and the International Union for the History and Philosophy of Science, the meeting reviewed recent research in Old World Archaeoastronomy. The publisher received the final typescript for production in March 1982. The papers on archaeoastronomy in the Americas are also published by Cambridge University Press in a companion volume, Archaeoastronomy in the New World, edited by A.F. Aveni. The papers in this book are concerned with shedding light on a controversial aspect of European prehistory, especially that of north-west Europe: was astronomy practised here in the late neolithic and bronze ages, and, if so, what was its purpose? These questions are of obvious interest to prehistorians, but modern interest in them has been stimulated largely by those whose professional background is in the pure and applied sciences, while they raise technical issues which have aroused the interest of statisticians and astronomers.
Archaeoastronomy in the Old World
Edited by D.C. Heggie
CAMBRIDGE UNIVERSITY PRESS Cambridge London New York New Rochelle Melbourne Sydney
CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521125307 © Cambridge University Press 1982 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1982 This digitally printed version 2009 A catalogue record for this publication is available from the British Library Library of Congress Catalogue Card Number: 82-4233 ISBN 978-0-521-24734-4 Hardback ISBN 978-0-521-12530-7 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
CONTENTS
PREFACE
vii
LIST OF CONTRIBUTORS
viii
INVITED PAPERS MEGALITHIC ASTRONOMY: HIGHLIGHTS AND PROBLEMS D.C. Heggie ARCHAEOLOGY AND. ASTRONOMY: J.N.G. Ritchie
AN ARCHAEOLOGICAL VIEW
THE STATISTICAL APPROACH P.R. Freeman STATISTICAL AND PHILOSOPHICAL ARGUMENTS FOR THE ASTRONOMICAL SIGNIFICANCE OF STANDING STONES WITH A SECTION ON THE SOLAR CALENDAR A. and A.S. Thorn MEGALITHIC ASTRONOMICAL SIGHTLINES: CURRENT REASSESSMENT AND FUTURE DIRECTIONS C.L.N. Ruggles
1 25 45
53
83
ASPECTS OF THE ARCHAEOASTRONOMY OF STONEHENGE R.J.C. Atkinson
107
IMPLICATIONS FOR ARCHAEOLOGY E.W. MacKie
117
PI IN THE SKY
141
H.A.W. Burl CONTRIBUTED PAPERS A SURVEY OF THE BARBROOK STONE CIRCLES AND THEIR CLAIMED ASTRONOMICAL ALIGNMENTS R.P. Norris, P.N. Appleton and R.W. Few OBSERVATIONS AT KINTRAW T. McCreery, A.J. Hastie and T.Moulds
171 183
DECODING THE CALLANISH COMPLEX - A PROGRESS REPORT M.R. and G.H. Pont ing
191
ASTRONOMY AND STONE ALIGNMENTS IN S.W. IRELAND A. Lynch
205
STONE RINGS OF NORTHERN POLAND R.M. Sadowski, M.S. Zio/kowski and K. Piasecki
215
CONTENTS
VI
ASTRONOMICAL ORIENTATION OF NEOLITHIC SITES IN CENTRAL EUROPE W. Schlosser and J. d e m y
225
STONE CIRCLE GEOMETRIES: AN INFORMATION THEORY APPROACH J.D. Patrick and C.S. Wallace
231
INVITED PAPER THE PRESENT POSITION OF ARCHAEOASTRONOMY C. Pedersen
265
INDEX
275
PREFACE
The papers in this book are concerned with shedding light on a controversial aspect of European prehistory, especially that of north-west Europe:
was astronomy practised here in the late neolithic and bronze ages,
and, if so, what was its purpose?
These questions are of obvious interest
to prehistorians, but modern interest in them has been stimulated largely by those whose professional background is in the pure and applied sciences, while they raise technical issues which have aroused the interest of statisticians and astronomers.
The diverse backgrounds of the authors of
these papers reflect the multidisciplinary approach which the subject deserves and, indeed, requires. The papers were presented at an international symposium on archaeoastronomy that was held at The Queen1s College, Oxford, from A to 9 September, 1981.
All the invited papers dealing with ancient astronomy in
the old world are included, except for one introductory paper on the astronomical background, and the volume also contains a wide selection of the contributed papers, some of which were presented as posters.
Papers
dealing with American archaeoastronomy will be found in a companion volume edited by A.F. Aveni. It is a pleasure to thank the authors of these papers for the time they have devoted to the preparation of their typescripts, and the staff of Cambridge University Press for their careful and expeditious production of this volume.
This is also a suitable opportunity to thank
the three bodies which materially supported the activities at the conference: the International Astronomical Union, the International Union for the History and Philosophy of Science, and the British Academy.
But particular
thanks are due to Michael Hoskin, who not only originally proposed the holding of the conference, but devoted much energy and good humour to its efficient organisation. Edinburgh 5 March 1982
Douglas C. Heggie
CONTRIBUTORS
P.N. Appleton: University of Manchester, Nuffield Radio Astronomy Laboratories, Jodrell Bank, Macclesfield, Cheshire SK11 9DL, U.K. R.J.C. Atkinson: Department of Archaeology, University College, P.O. Box 78, Cardiff CF1 1XL, U.K. H.A.W. Burl: 40 St. James Road, Edgbaston, Birmingham B15 1JR, U.K. J. Cierny: Ruhr-Universita't, D-4630 Bochum, West Germany R.W. Few: 147 Girton Road, Girton, Cambridge CB3 OPQ, U.K. P.R. Freeman: Department of Mathematics, The University, Leicester LEI 7RH, U.K. A.J. Hastie: Cardonald College, 690 Mosspark Drive, Glasgow G52, U.K. D.C. Heggie: Department of Mathematics, University of Edinburgh, Kingfs Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K. A.Lynch: National Monuments, Office of Public Works, 51 St. StephenTs Green, Dublin 2, Ireland T. McCreery: Cardonald College, 690 Mosspark Drive, Glasgow G52, U.K. E.W. MacKie: Hunterian Museum, The University, Glasgow G12 8QQ, U.K. T. Moulds: 9 Park Road, Glasgow, U.K. R.P. Norris: University of Manchester, Nuffield Radio Astronomy Laboratories, Jodrell Bank, Macclesfield, Cheshire SK11 9DL, U.K. J.D. Patrick: Department of Computer Science, Deakin University, Victoria 3217, Australia 0. Pedersen: History of Science Department, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark K. Piasecki: Zakiad Antropologii Historycznej UW, Krakowskie Przedmiescie 1, 00-927 Warszawa, Poland G.H. Ponting: T01cote', Callanish, Isle of Lewis, PA86 9DZ, U.K. M.R. Ponting: 'Olcote1, Callanish, Isle of Lewis, PA86 9DZ, U.K. J.N.G Ritchie: The Royal Commission on the Ancient and Historical Monuments of Scotland, 54 Melville Street, Edinburgh EH3 7HF, U.K. C.L.N. Ruggles: Department of Archaeology, University College, P.O. Box 78, Cardiff CF1 1XL, U.K. R.M. Sadowski: ul. Mi^dzynarodowa 33 m. 24, 03-962 Warszawa, Poland W. Schlosser: Ruhr-Universita't Bochum, Astronomisches Institut, Postfach 102148, D-4630 Bochum 1, West Germany A. Thorn: The Hill, Dunlop, Kilmarnock KA3 4DH, U.K. A.S. Thorn: The Hill, Dunlop, Kilmarnock KA3 4DH, U.K. C.S. Wallace: Department of Computer Science, Monash University, Clayton, Victoria 3168, Australia M.S. Zi6ikowski: Zakiad Antropologii Historycznej UW, Krakowskie Przedmiescie 1, 00-927 Warszawa, Poland
MEGALITHIC ASTRONOMY:
HIGHLIGHTS AND PROBLEMS
D.C. Heggie 3 St Ninian's Terrace, Edinburgh EH1O 5NL, U.K.
Abstract. After a discussion of the need for statistical methods in megalithic astronomy, the interpretation of statistical results is considered, and a simple method of performing a suitable statistical test is outlined. Statistical evidence is considered next, with particular regard to the extent and' limitations of the role of selection effects in the work of the Thorns. Their most recent analysis of lunar lines is discussed. Some arguments of a practical nature then follow, and the paper ends with some briefer comments on the astronomical interpretation of megalithic art, dating, and the purpose and implications of megalithic astronomy.
INTRODUCTION The present paper is a rewritten version of a review article (Heggie 19-8lb) which was designed as an introduction to problems of megalithic astronomy for participants at the conference in Oxford.
However
the resemblance is largely confined to the title and the structure.
Its
general purpose here is to provide a background for many of the other papers in the present volume, but the opportunity is also taken to argue the case for the use of a particular methodology in the examination of much of the evidence on megalithic astronomy, and to consider how it may be applied to one or two important bodies of data.
Another purpose of this
paper is to draw the attention of readers to a number of recent results which have a bearing on the subject and are perhaps not mentioned elsewhere in this volume.
On the other hand nothing is said of the archaeological
background to these studies, which is one of the purposes of the paper by Dr Ritchie, and little space is devoted here to the numerous important archaeological arguments which bear on the interpretation of the evidence; but many of these are discussed by several of the authors who have contributed to this book. The idea that astronomy was one element in the function of certain megalithic sites in Britain and elsewhere is an old one, as Prof.
Heggie: Megalithic astronomy: highlights and problems
2
Atkinson mentions in his paper, but it has never flourished more vigorously than in the last two or three decades, thanks largely to the work of Prof. Alexander Thorn.
Though his work had begun in the 1930s, it was not until
195*+ that his first paper on the subject of prehistoric astronomy appeared. In 1967 he published a book (Megalithic Sites in Britain) in which evidence from some hundreds of sites was collated (Fig.l).
Much new evidence was
then produced in two subsequent books (Thorn 1971;
Thorn & Thorn 1978a),
where particular emphasis was laid on very accurate sightlines for the moon using distant markers, mostly natural. The present activity in the field of archaeoastronomy in the Old World, or at least in the British context, can be seen largely as the response of experts in different disciplines to Thorn's work.
Among
archaeologists some, such as Aubrey Burl, have selected the parts of Thorn's ideas which can be absorbed most readily into a fresh but relatively conventional picture of the societies of the megalith builders.
A few,
notably E.W. MacKie, have considered in a more radical way what changes in the conventional picture would be required by Thorn's theories.
And it must
be admitted that there are many archaeologists, who do not attend conferences on archaeoastronomy, who consider that his theories shed no light on these problems, for all the acknowledged excellence of his field surveys. Finally there are those with less archaeological experience, or, more often, none at all, who have responded actively to the more technical aspects of Thorn's work, such as the statistical evaluation of his theories, and the associated problems of ensuring that the available data are suitable.
But
Prof. Thorn's work has not been limited to the astronomical aspects of megalithic sites, and if the response to his work on megalithic geometry has been less vigorous, it is because the necessary methods of analysing his work in this field have proved much harder to develop.
(Dr Patrick's
paper in this volume marks a significant breakthrough in this respect.) Nor is Thorn's influence confined to Britain, as many of the American archaeoastronomers at the Oxford symposium testified warmly to the great interest which his work has engendered in the New World also.
STATISTICAL ARGUMENTS The need for statistical methods The great bulk of the evidence on megalithic astronomy consists of orientations, alignments, or 'lines', directed towards a place on the horizon where a conspicuous astronomical object (sun, moon, a planet, or a
Heggie: Megalithic astronomy: highlights and problems
bright star) rises or sets.
Of course the rising and setting positions of
the sun, moon and planets vary relatively rapidly, and so for them it is the extreme rising and setting positions that are generally considered. For the sun the extreme positions are those reached at the solstices, but several authors have also considered orientations for the sun at other
Fig.l.
2
The astronomical sites listed in Thorn 19-67 •
Heggie: Megalithic astronomy: highlights and problems
4
times of the year, as discussed, for example, by the Thorns in their paper in this volume.
The rapid and relatively complicated motion of the moon
makes its extremes rather involved, but at a low level of accuracy the extreme positions are simply the 'standstill1 positions, to use the convenient term introduced by Thorn (19T19 p.l8).
Extreme positions for the
planets may also be defined, but in fact the planets have been rarely discussed in this context. Coupled with this variety of astronomically significant positions is an equally broad choice of megalithic orientations.
These
may be defined by single slabs, true alignments of standing stones, lines from the centre of a stone circle to an outlying stone, lines from one site to another, the axes of megalithic tombs, lines from a prehistoric site to a natural horizon feature (or 'foresight'), such as a hill-slope, a valley or notch, and so on. Given this great diversity of 'targets' and orientations, one must consider the possibility that it is only by chance that one finds some sites to be astronomically orientated.
Indeed we can be virtually
certain that coincidences occur, and since we do not know a priori that the megalith-builders were interested in any particular astronomical object, it seems wise to dismiss any apparently astronomical orientations as coincidences unless there is evidence to the contrary.
If we relax this attitude
(and it must be said that many authors have never adopted it in the first place) then we shall be in grave danger of writing books and papers whose rightful place is on the fiction shelves.
The fact that it has been
ignored so often possibly accounts for the general air of controversy in which debates on megalithic astronomy tend to have been conducted.
If
indeed a body of evidence does not allow us to conclude that the orientations involved are not just coincidences, it is perhaps to be expected that an enthusiastic archaeoastronomer and a careful archaeologist can come to diametrically opposed conclusions. The stress which is laid on statistical methods here (and in Prof. Freeman's paper in this volume) reflects the nature of the evidence available for the study of megalithic astronomy.
One can imagine plausible
circumstances in which the importance of such methods might be much diminished.
In his paper in this volume Dr MacKie expresses the hope that a site
might be found which, on excavation, decisively supports only an astronomical interpretation.
Were such a site to be found then statistical evidence
would have only a small role to play with regard to that site and others
Heggie: Megalithic astronomy: highlights and problems
like it.
5
But at present no such key site is known, and the great bulk of
the evidence requires statistical evaluation if we are not to be misled by it.
The study of Mayan astronomy, on the other hand, exemplifies a field
where the statistical evaluation of orientations is of relatively minor importance, because information from orientations is supported by evidence of the most decisive kind, in the form of a decipherable astronomical notation.
At the Oxford conference, several European participants voiced
some dismay at the lack of statistical analysis of the evidence on native American astronomy, but it may be argued that this reflects the rather supplementary role which the study of orientations plays in much of this work.
The great difference
in the nature of the evidence available on
the two sides of the Atlantic is one of the points to which Prof. Pedersen also draws attention in his paper in this volume. In the context of megalithic astronomy, other evidence of a decisive kind (i.e. apart from orientations) has not yet turned up, and orientations are the basic evidence on which the hypotheses have to be tested.
And to establish that the orientations one finds are not coincid-
ences one has to show, if possible, that one finds more orientations towards phenomena of astronomical importance than would be expected to occur by chance.
The most important role of statistics in this context is, in
effect, to calculate the probability of obtaining by chance a number of orientations not less than the number actually found in the investigation under study.
If the orientations have nothing to do with astronomy and
are essentially random, then the probability thus found is unlikely to take very low values.
Sometimes, as with the statistical test devised by
Freeman & Elmore (1979)» "the results are not expressed directly in terms of probabilities, but they can still be interpreted qualitatively in much the same way.
Interpretation of statistical results Before considering how the probability is to be calculated, we must discuss how the results are to be interpreted.
If the probability
obtained is not very low, then we have little reason to reject the notion that the orientations are random.
(This is not to say that the orientations
are not deliberate, however, for one might contemplate the suggestion that the sites were orientated on non-astronomical objects, such as hills, or sacred places, or routeways.
The point is that, even if such a suggestion
were correct, we would have no reason to expect more orientations with
Heggie: Megalithic astronomy: highlights and problems
6
apparent astronomical significance than we would expect from a genuinely random set.)
If, on the other hand, the probability turns out to be very
small, then we have strong grounds for rejecting the notion that the orientations are random, but we must take care before coming to the obvious conclusion that they are genuinely astronomical.
Low levels will occur
only rarely if the orientations are random, but they will occur.
In the
same way, if we look through enough sets of randomly generated data, we will be able to select one or more which look very non-random.
This is the
lesson which the rather outre example in Dr MacKie's paper in this volume ought to teach us.
Unless our data have been selected objectively, the
obvious conclusions may easily be false ones, and Aubrey Burl's recommendation (see his paper in this volume) that one should study groups of monuments, rather than individual examples selected from such groups, can be seen as a safeguard against this. The most important selection effects that can endanger the statistical analysis of megalithic orientations are concerned with the selection of the sightlines themselves.
It has been realised for a long
time (Thorn 1955) that it is difficult to be objective about this, and it is no less difficult to try to apply strict selection criteria retrospectively.
Nevertheless this must be attempted if we are to derive meaningful
conclusions from most of the existing evidence for megalithic astronomy, at least until we possess fresh bodies of data prepared according to stricter selection criteria.
(in his paper in this volume Dr Ruggles offers us
precisely this prospect.) This emphasis on selection criteria should not obscure the other problems associated with the statistical investigation of orientations, though they are often more easily overcome.
For example, one must try to
minimise the influence exerted by the data on the formulation of the particular astronomical hypothesis to be examined.
A simple statistical method Finally we come to the way in which the probability is to be calculated, i.e. the probability that a set of random orientations would yield (by chance) the number of astronomically significant lines that we actually find, or even more.
A simple and rough (but widely applicable)
method of doing so will now be described. Several pieces of information are required, namely (i)
the tolerance, t, i.e. how closely an orientation must agree with an
Heggie: Megalithic astronomy: highlights and problems
astronomically significant direction to be included.
7
The tolerance may
depend on the accuracy with which the direction of the orientation can be defined, in which case it will generally be expressed in terms of azimuth. But it may also be expressed in terms of declination, and then it can be converted approximately into an equivalent tolerance in azimuth by multiplying by the quantity |dA/d6| (the rate of change of azimuth with declination).
For many approximate purposes this may be read from Fig.2.
As an
example, an orientation to some point on the sun's disc at a solstice must t
indicate a declination within approximately l6
of that of the sun's centre,
i.e. the tolerance in declination is 16 , since this is the mean apparent radius of the disc.
Since the declination is about 2^°, at the latitude of
Stonehenge (51?2) |dA/d6| is about 1.9, leading to a tolerance in azimuth of about 30 .
Fig.2. The factor |dA/d6|. The graph is entered by declination (5) and latitude (A). The curves were calculated for the case of zero horizon altitude, and the sign of the declination is irrelevant. It is not possible to obtain accurate values from these graphs at declinations close to the colatitude (90°-X).
\ II
>/ /
_1 J_ 7
7_
o
/
j
/7
1 dA dl
y
0
1
/
/
y
^
^
_ — - "
r
* , — —
-
—•
_ _ — -
-
i
1
.
. — -
_ —
—
•
~-—
— — •
•
- •
10
20
30
40
Heggie: Megalithic astronomy: highlights and problems
(ii)
the number of astronomically significant positions.
8
These must be
chosen fairly (Hawkins 1968), so that if the position of sunrise at the equinox is included, then so must the position at sunset.
Again, if we
wish to test the hypothesis of the solstitial orientation of the axis of Stonehenge, we must include both sunrise and sunset at both solstices, i.e. four positions in all. (iii)
the probability, p, that a single random orientation would be regard-
ed as astronomically significant.
In straightforward cases this is simply
the number of significant positions times twice the tolerance in azimuth (since an orientation may deviate on either side of the precise astronomical direction under consideration), divided by 360 .
If we are testing the
solstitial hypothesis for the orientation of the axis of Stonehenge, then p = ^1x2x30 /36O° = 0.011, approximately. (iv)
the total number of orientations, N, in the sample, i.e. including
both astronomical and non-astronomical orientations.
What is actually need-
ed is the total number of available orientations from which the sample was selected, and it is often difficult to find information on this.
Indeed it
is at this point that it is frequently necessary to make some allowance for unwritten or faulty selection criteria.
In the case of the axis of Stone-
henge, however, it is clear that one should take N=l, since the axis is much the most clearly defined orientation at Stonehenge, and may be regarded as the unique principal orientation of the monument (cf. Prof. Atkinson's paper in this volume). (v)
the actual number, n, of astronomical orientations in the sample.
For
example, since the axis of Stonehenge does actually indicate a point on the sun's disc at the position of midsummer sunrise at the time of its construction (this can be inferred from the data given by Thorn & Thorn 1978a, p.150), we have n=l. Now we have to calculate the probability, P, that at least lines out of a sample of
N
nomical position within the stated tolerance.
If
n
and
N
are both 1,
as in the test of the axial orientation of Stonehenge, then obviously In other cases,
P
n
random orientations will indicate some astro-
P=p.
may be calculated from expressions based on the binomial
distribution (the standard formula is given, for example, in Heggie 198la, p.2l+2), or from an approximation based on the - Poisson
distribution.
For the latter purpose we need also (vi)
the expected number, n , of astronomical orientations, which is just
the average number that would be expected to occur in a sample of
N
random
Heggie: Megalithic astronomy: highlights and problems
Fig.3. Probability, P, of obtaining at least n astronomical orientations by chance. The average number that would be expected by chance is denoted by n . Above the line P = 0.001, the value of P is below 0.001; below the line P = 0.1, the evidence for astronomical orientations is not statistically significant. For restrictions on the applicability of this graph see the text.
35
30 20
7
7
7
-•
10 8 7 6
,/
y
/
y
/ /
^y
y
• '
r
'' /
/
* /
/
y
/
/ /
/
/
/
*
y ^y w
c6
y y
y
A
s
.1
•4
5
-tn
Heggie: Megalithic astronomy: highlights and problems
orientations, i.e. n
= Np.
If
N
is large and
n
10
is small then the
Poisson approximation is satisfactory, and then the probability read from Fig.3, "which is entered by the expected number
n
P
can be
and the excess
of the actual number over the expected number, i.e. (n-n ) . Actually, the probabilities obtained from this graph are also approximately correct in other circumstances, e.g. when any restriction on (n
N.
n = 1
and
n
is very small, but without
Indeed the correct result for the Stonehenge problem
= 0.011, n = l) can be obtained approximately from this graph.
STATISTICAL EVIDENCE Early statistical investigations Some of the earliest statistical arguments are to be found in a book by R. Miiller published in 1936.
One of the sites to which they were
applied is a group of rings at Odry (near Czersk, Poland), but in fact these are much younger than the sites normally considered in studies of megalithic astronomy (see Dobrzycki 1963, and the paper in this volume by Sadowski et_ al.).
Millie r also rediscussed some earlier statistical results on a group
of lines by J. Hopmann, and showed that nothing of statistical significance survived when one took into account all the possible sightlines - an early case of retrospective correction for selection effects. Now we come to the early work of Professor Thorn.
His first
paper on megalithic astronomy (Thorn 195M contained no statistical analysis of the type we are considering, but such an analysis, using the data from this paper, has been attempted recently (Heggie 198la, pp.l53f.), and the conclusions are as follows.
Formally there is statistically significant
evidence for solstitial orientations (of three distinct structural types, but analysed together) in Thorn's paper.
This is true even if we are rather
strict in omitting sightlines over which, in Thorn's opinion as expressed here and in later books and papers, some doubt exists.
Furthermore Thorn's
own selection criteria in this paper seem to have been quite strict, to the extent, incidentally, of excluding sightlines (such as that to the southwest at Ballochroy, Argyll) which have been brought subsequently to some prominence in later papers and which, if retained, would have strengthened the evidence for megalithic astronomy.
These solstitial sightlines also
strongly suggest that it was not just any point of the solar disc, but one or other limb, towards which they were directed, though no probability level was calculated for this result. Professor Thorn's second paper dealing with megalithic astronomy
Heggie: Megalithic astronomy: highlights and problems
11
appeared in 19555 and contained (for the first time in his work) an analysis of the statistical significance of the evidence, in relation to solstitial and equinoctial sightlines taken together.
What was also new about this
paper, however, was the discussion of possible stellar lines.
Now since
there are so many stars, and since their rising and setting positions vary by such large amounts over the period in which the megalithic sites were built, several writers have been apt to dismiss any talk of stellar orientations out of hand on the grounds that these can so easily be coincidences. The fact that such comments are rarely challenged demonstrates that this early paper of Thorn's has not received the attention that it certainly deserves, for in it he shows that the number of stellar orientations which he found greatly exceeds what would be expected in a comparable sample of random orientations.
This excess occurred only for a narrow range of dates -
about 2100 B.C. As usual with such studies, it is wise to examine this investigation carefully, to ensure that the result is not obviated by selection effects.
In fact the sightlines were of two types, but Thorn himself noted
a number of difficult, borderline cases, and a re-examination of the selection of the sites in this paper (Heggie 198la, pp,157f.) raises similar doubts over other sites which Thorn did not specifically note as posing any difficulty.
However, as Dr Ruggles points out in his paper in this volume,
Thorn did remark in his paper that 'nothing has been excluded which has a bearing on the subject', and it may be that selection effects play a relatively insignificant role.
The evidence in Thorn's first book The next major publication by Prof. Thorn was the epochal 'Megalithic Sites in Britain' (1967).
This book contains, besides numerous
comments on individual sightlines, a master list of over 250 lines ('Table 8.1') from almost 150 sites (Fig.l).
It must be stressed that Thorn himself
did not attempt to use this data for any quantitative estimates of statistical significance, but several later writers have quoted this list of sightlines and an accompanying histogram ('Fig.8.1') as powerful evidence for the practice of megalithic astronomy.
What has generally been neglected in such
assessments is any consideration of the nature of the criteria according to which these lines were selected for inclusion.
Thorn himself recognised the
varying reliability of these, by assigning each line to one of three classes, from class A (which includes the most reliable lines) to class C.
The latter
Heggie: Megalithic astronomy: highlights and problems
12
includes lines which are admitted merely because they indicate a declination of astronomical significance, and of course it would not be possible to use these for a fair statistical test of the astronomical hypothesis, as Thorn mentions.
Nevertheless questions about the selection criteria, which are
discussed in a general way by Dr Ruggles in his paper in this volume, are not restricted to class C, but apply also to some lines of class A, as the following examples suggest. At Ballochroy (Argyll) one of the three stones indicates a natural foresight (in this case a hill-slope) for midsummer sunset, and this is assigned to class A.
However, one of the other stones also indicates a hill-
slope, but in this case no astronomical interpretation is known (MacKie 197*0, and this line is not included in Thorn's list at any level of reliability. Thorn accounts for this (pers. comm.) by noting that the central stone is the taller of the two.
However it was MacKie's view that 'if one considers
the site without foreknowledge or preconceived ideas there is no reason from its layout to prefer either
f the indicated alinements as the primary
solstitial one', and so the line i licated by the shorter stone should have been included at least in class B, which 'contains borderline cases which some people might accept and others discard' (Thorn 1967, p.96). Another example occurs at Castle Rigg (Cumberland), where two of the four sightlines (all of which are of class A) are provided by one of the special diameters, used in both directions, in Thorn's geometrical construction for this ring.
Both sightlines have an astronomical interpretation.
However the other special diameter (symmetrically disposed with respect to the first) is not listed in either direction in any class.
Its ends, like
those of the listed diameter, are marked by stones, one of these being one of the tall entrance portals (Burl 1976, pp.58-9; this paper, Fig.U).
Also,
the horizon altitudes (information on which can be found in Thorn 1966, Fig. 39) are comparable, and the unlisted diameter is notable for its indication of a very prominent foresight to the north.
To the south it could perhaps
have served as an indication of the moon at the major standstill, but to the north it could not have indicated any of the astronomical declinations considered by Thorn in his book. A third example which illustrates the selection difficulties in the list in Thorn's book is the little alignment at Doune (Perthshire), of which photographs will be found in Heggie 198la, p.l6l.
Though details of
the alignment in both directions were quoted in an earlier paper (Thorn 1955) 3 only the line to the north was listed in the book, where it was assigned to
Heggie: Megalithic astronomy: highlights and problems
class A.
13
In this direction the line can be identified with the star Capella,
but to the south it indicates none of the astronomical declinations considered in the book.
Evidence on accurate lunar lines Since the time of publication of his first book, Prof. Thorn's attention has been much taken up with the study of supposed very accurate lunar lines.
One of the first of these studies to have been tested statist-
ically was his work on the lunar 'observatory' using Le Grand Menhir Brise", near Locmariaquer (Brittany), as a foresight.
The result (Freeman 1975)
was that there was nothing of significance to be explained if the number of potential backsights (i.e. possible observing positions) exceeded about
Fig.^i. An unlisted sightline at Castle Rigg, viewed from the north. The line, which is a diameter of Thorn's geometrical construction for this ring, runs from the east portal (foreground, right) to the middle stone of the group of three on the far side of the ring. The other (symmetrically disposed) diameter is illustrated in Heggie 198la, pp.112,113.
Heggie: Megalithic astronomy: highlights and problems
two hundred.
14
It was the need to make retrospective allowance for possible
effects of selection of backsights that led to a conclusion of this form. Actually doubts have been voiced over even those backsights that were chosen (Hadingham 198la), and over the foresight, since there is no record that the Menhir ever stood upright (see Burl 1976, pp.129-30), though there are certainly arguments for supposing that it did (Atkinson 1975;
Merritt
& Thorn 1980). The Thorns have identified many other possible lunar sightlines of high accuracy, and have used these to test the theory that the purpose of the lines was to record fine variations in the extreme declinations of the moon caused by solar perturbations.
If this theory is correct, one
expects the indicated declinations to be concentrated at particular values within the so-called lunar 'bands' (which are defined by the Thorns in their paper in this volume).
If, on the other hand, the lines were at most rel-
atively rough indications of the lunar extremes, and the perturbation was not observed, then one might expect the indications to be relatively randomly distributed over the bands.
In fact from several analyses (Thorn & Thorn
1978a, p.136; 1978b; A.S. Thorn 198l) the Thorns have concluded that the latter hypothesis must be rejected, and that the indicated declinations are concentrated, at a high level of statistical significance, towards the values expected on the hypothesis which they proposed.
But they have also
expressed surprise that the indicated declinations lie as close to the expected values as they do, because the agreement seems closer than one would think possible on practical and other grounds (see also Heggie 198lb). It may be that an explanation of this difficulty is to be sought in selection effects.
When some attempt is made to allow for other potent-
ial combinations of backsights and foresights at a few much-studied sites such as Temple Wood in Argyll and Brogar in Orkney (see Heggie 198la, pp. 172f.) - it appears that the number of indicated declinations close to the expected values is not so different from what would be expected if the indicated declinations were randomly spread over the lunar bands.
A thorough
examination of selection effects has yet to be completed (Ruggles 1983) , but the foregoing examples are surely indicative.
Furthermore the analysis
made by the Thorns is quite sensitive to the selection of the foresights. For example, their formally most significant result (A.S. Thorn 198l) concerned h2 sightlines, and for this sample the probability of obtaining such close agreement with the ideal declinations is about 10
-h
. But if one added
only another dozen or so foresights indicating declinations within the lunar
Heggie: Megalithic astronomy: highlights and problems
15
bands, but far from any of the ideal declinations, it would no longer be possible to conclude that the indicated declinations were non-random, at any level of significance.
It cannot be argued that the selection of fore-
sights is complete to anything like this extent.
The Thorns' new analysis It is the problem of the influence of selection effects in previous analyses which makes the new analysis reported by the Thorns in their paper in this volume so important.
Here sightlines are divided into
three classes, depending on the sign of A (the solar perturbation) in the expression for the declination, 6, of the centre of the moon in terms of e (the obliquity of the ecliptic), i (the mean inclination of the lunar orbit), and A.
(A lucid discussion of the meaning of these quantities will be found
in Morrison 1980.) (F), those where
Lines for which 6 = _+ e +_ (i+A) 6 = ±e +_ (i-A)
line is not relevant if
are called 'favourable'
are called 'unfavourable' (U), and the
6 = +e +i.
The important point is that the con-
cept of favourable and unfavourable lines was formulated after the selection of the foresights was made, and so could not have influenced the selection.
Hence, the argument runs, if the foresights were distributed at
random there should be on average equal numbers of
U
and
F
declinations,
whereas the actual numbers are significantly different. A couple of detailed remarks may be made about this.
First,
when one examines the ideal declinations listed by the Thorns (the paper in this volume, Table l ) , the range of declinations corresponding to lines is found to exceed slightly the range corresponding to which makes their result still more significant.
F
U
sight-
sightlines,
Secondly, however, when
one talks of a random distribution of foresights in the lunar band, one is thinking of foresights distributed at random in azimuth.
The distribution
of indicated declinations is therefore proportional to the factor |dA/dS| plotted in Fig.2.
Now this factor increases as the arithmetic size of the
declination increases.
Since the favourable and unfavourable declinations
are different, a uniform distribution of azimuths gives rise to different distributions of declinations near the favourable and unfavourable values. The effect is negligible for the minor standstill, but is more significant for the major standstill, especially at high latitudes when the foresight is at a high altitude in the southern half of the horizon.
At a very few
sites the effect is so strong that the probability of obtaining a favourable declination may exceed about 0.6.
Nevertheless such a case is exceptional,
Heggie: Megalithic astronomy: highlights and problems
16
and it has been estimated that the average value of the probability is about 0.53 (when account is taken of both effects referred to in this paragraph). This implies that the expected number of favourable declinations in the Thorns' sample of 51 lines increases from 25.5 to about 27.0.
This change
is large enough to alter their probability level by a very substantial factor (which can be estimated from Fig.3), but not by so much as to convince one that the result can be explained away. It may well be, then, that we here have significant evidence for an excess of favourable over unfavourable foresights.
But the infer-
ence to be drawn from this may well only be that, while the unfavourable foresights are coincidences, a few of the favourable ones are intentional. If so, then what we may infer is only that there are deliberate foresights for the moon when the declination of its centre is
6 = +e j+(i+A);
although this expression contains the perturbation term
and,
A, we are not able
to infer that the variation caused by the perturbation was observed, but only the extreme declination, which occurs when the perturbation is at maximum.
The possibility of such a conclusion (on other grounds) was also
considered by Morrison (1980), and it could remove the need for methods of extrapolation (Thorn 1971, ch.8) and associated problems.
But while our
tentative conclusion may seem a rather modest one, it could be quite important.
Previously it was thought by many that the best evidence for
sightlines to the extreme lunar declinations was that contained in Thorn (1967,chapter 10), but this evidence no longer seems very sound (Ruggles 198l).
Therefore, if, as is suggested here, the new discussion of favour-
able and unfavourable foresights lends some support to the same conclusion, then this discussion may be of some importance. One may ask, with all the attention devoted to lunar lines in the last decade, what has happened during that period to Thorn's earlier astronomical theories?
As far as solar or calendrical sightlines are con-
cerned, the answer will be found in the Thorns' paper in this volume.
But
stellar lines have been a casualty of their revisions over the years.
One
particularly conspicuous group of stellar lines in the 1955 paper was reinterpreted as being calendrical (Thorn 1967, p.103), and some other stellar lines were reassigned to the moon (those discussed in Thorn & Thorn 1978a, p.5, and one or two others discussed in Thorn 1955 which might at that time have been identified with the star e Canis Majoris, or Adhara).
If the
discussion of possible selection effects in the later work has the effect of diminishing the support for the lunar theory, then the time may come for
Heggie: Megalithic astronomy: highlights and problems
a reexamination of these earlier interpretations.
17
Certainly they were
based on a sample of sightlines whose selection has not yet been called into such serious question, and their statistical significance is relatively clear.
Other statistical research There are several statistical investigations which have not been mentioned here.
But the statistical evidence on Stonehenge has been
summarised recently (Heggie 198la, pp.l^5f., pp,196f.), and the possible astronomical aspects of this monument are the subject of Prof. Atkinson's paper in this volume.
Much of Aubrey Burl's recent work, which can be
traced through his paper in this volume, is susceptible to statistical analysis, where conclusions are not obvious from a visual inspection of the data.
Several other papers in this volume also contain evidence of a stat-
istical nature, including those by Freeman, Norris et al., and Lynch. Particular mention must also be made here of some other recent statistical investigations of prehistoric astronomy in Europe, those of grave orientations in cemeteries.
Though not concerned with megalithic
monuments, these studies certainly rely on evidence which, in its nature and its analysis, closely resembles that for megalithic astronomy, and two papers at the Oxford symposium were devoted to this material.
An account
of the work of K. Barlai on Hungarian sites is already in print (Barlai 1980), and the present volume contains a paper which summarises results by W. Schlosser and J. Cierny on some different sites in central Europe.
NON-STATISTICAL ARGUMENTS The statistical method offers a rational way of deciding how well the distribution of orientations agrees with some variant of the astronomical hypothesis;
and since most of the influential work on mega-
lithic astronomy rests on the presentation of data showing that orientations appear to agree with astronomically significant directions, the statistical examination of these results is bound to play an important role.
But there
are several other yardsticks against which the hypotheses can be. measured, such as feasibility, and some types of evidence can have a bearing on the subject in a way that is not amenable to statistical analysis. purpose of this section to consider a few of these arguments.
It is the
Heggie: Megalithic astronomy: highlights and problems
18
Practical arguments Questions of the visibility of suggested foresights at certain sites have led to some interesting results.
One concerns a supposed lunar
line to the south at Callanish 1, in the Outer Hebrides.
The line in quest-
ion consists of an accurate foresight for the moon (Thom 1967, pp.12^-5) which is indicated by the avenue at Callanish 1.
But it has been known for
some time (Hawkins 1971) that the view of the foresight from the avenue is obscured by an outcrop of rock to the south of the site. see Burl 1976, p.151, and Roy 1980.)
(For illustrations
This led Hawkins to suggest (Hawkins
1973, p.2i+0) that the intention was to make the moon appear to set into this rock, and the Pont ings have suggested that the site might have been arranged deliberately so that the moon set within the stones of Callanish 1 (see Fig.2 of their paper in this volume), an
idea that parallels Burl's
suggestions about the possible lunar orientation of certain recumbent-stone circles (Burl & Piper 1919, p.36).
The presence of the obscuring outcrop
tends to detract from the idea that the foresight might have been used for precise observation of the moon, a possibility that is weakened further by an argument about extrapolation (Heggie 198la, p.195).
This problem of the
visibility of the foresight at Callanish incidentally illustrates something which is rather typical of such structural arguments:
rather than allowing
us to conclude that astronomy was not practised at a site, an argument of this kind is usually more of a clue to the nature and purpose of any astronomy practised there. But there is one site at which the problem of the visibility of a foresight led to discoveries of a quite unexpected and intriguing nature. At Kintraw, Argyll, the visibility of the solstitial foresight from the backsight was found to be inadequate because of an intervening ridge (Thorn 1967 5 p.155), and so it was suggested (Thorn 1969) that observations were made from a ledge in the hillside behind the site.
E.W. MacKie then made
the remarkable discovery by excavation of a layer of stones on this ledge (MacKie 197*0, "but acceptance of the implications of this work has been hindered by two things.
One is the absence of clear evidence, in the form
of artefacts, for instance, that the layer of stones is artificial, but the other was a persistent problem over the visibility of the foresight from the ledge.
MacKie found that the mountain which forms one side of the foresight
'can be seen clearly over the ridge (in good weather)', and published a photograph illustrating the fact (MacKie 1977 9 p.106).
J.D. Patrick, on the
other hand, 'could not satisfy himself that it was possible to see the base
Heggie: Megalithic astronomy: highlights and problems
19
of the notch using a theodolite with 30 power magnification', a statement again accompanied by an illustrative photograph (Patrick 198l).
Now the
paper in this volume by McCreery et al. goes a long way towards resolving this disagreement:
it seems that both authors are right, but only some of
the time. Another piece of evidence based on practical considerations, and one that is not amenable to any statistical calculation, is the siting of two of the mounds at the Ring of Brogar, Orkney (see the paper by the Thorns in this volume).
On the other hand, one practical argument which has
tended to be forgotten in recent years is the need for adequate space for extrapolation, at sites which are considered to be accurate lunar observatories (Thorn 1971» chapters 8,9). For the foresight to the north-northwest at Brogar, i.e. Ravie Hill, the extrapolation length UG (in Thorn's notation) is about 0.8 km.
If, therefore, observations were made by moving at
right angles to the line of sight, some observations must have been taken from boats on the Loch of Harray - a most novel form of megalithic backsight!
Astronomical interpretation of megalithic art These practical arguments are concerned with orientations and associated questions, and the bulk of the evidence on megalithic astronomy is of this nature.
But there are independent pieces of evidence for which
statistical methods are of no avail.
An example is what has been called
the 'Calendar Stone' at Knowth (Co. Meath), which has been described recently (amid much nonsense, it must be said) by Brennan (1980, p.98).
On the
upper half of this stone (Fig.5), along with other markings, is a roughly oval sequence of 29 symbols.
The seven uppermost symbols are either a
circle or a pair of nested circles, and the remainder, which mostly extend in a horizontal row along the middle of the stone, are crescents.
This
design can be interpreted as a cycle of symbols representing the motion of the moon through one synodic month (new moon to new moon) of 29.5 days, with a rough representation of the phases and of their typical relative prominence. Although the designs and markings on some other megaliths have often been interpreted in astronomical terms, no example is as persuasive as this. One case which has been shown recently to be false is Muller's interpretation (Miiller 1970, p. 107) of the markings on an orthostat in the tomb called 'Table des Marchands', close to the Grand Menhir.
According to Miiller there
are 56 individual markings, which represent the years of three nodal cycles of the moon, as with the 56 Aubrey Holes at Stonehenge (Hawkins & White
Heggie: Megalithic astronomy: highlights and problems
20
, pp.lTTf. ), but it has been pointed out (Hadingham 198lb) that there are, quite simply, fever than 56 symbols on the stone, and perhaps only k9.
MEGALITHIC ASTRONOMY IN THE WIDER CONTEXT The study of megalithic astronomy is part of the study of megalithic monuments in general, and this is the business of prehistorians and archaeologists.
Therefore everyone involved must be concerned to ensure
that sound results on megalithic astronomy can be properly encompassed within the larger field of enquiry.
The observation, often made, that non-
archaeologists researching into the subject ought to acquaint themselves better with what archaeologists have found out, is one to which all would give their assent, but there are broader aspects of archaeological thinking (for example, on the nature of the societies in question, or on the relationships between monuments of different types) of which the typical nonarchaeologist's view remains ill-focussed and fluid.
Here it is difficult
for the non-archaeologist, and perhaps unwise, to do more than pass the odd comment, and to ensure that the discussion is based on sound facts and straightforward interpretations, to the extent that this lies within his competence. One obvious area of contact is dating.
Commenting on the prev-
ious version of this paper, Dr Ritchie kindly pointed out that it was wrong to imply that anything could be inferred about the date of Brogar from the
Fig.5. A possible lunar representation on the 'Calendar Stone', Knowth (schematic, after Brennan, 1980).
Heggie: Megalithic astronomy: highlights and problems
21
radiocarbon dates obtained for the nearby monument at Stenness, and so there was no conflict with the narrow range of dates for Brogar inferred by the Thorns on astronomical grounds.
Actually the Thorns also regard Sten-
ness itself as a lunar backsight (Thorn & Thorn 1978a, p.130) at a date close to those assigned for the lines at Brogar, i.e. within about 150 years of lh60 B.C., some 1500 years after the dates for Stenness.
But strictly there
is no contradiction, since the foresight for Stenness is a cairn, and it may have been this rather than the backsight which was positioned to define the sightline. If the lunar line at Stenness is not simply an accident, it exemplifies one of the problems confronting the archaeologist when he tries to integrate the evidence for megalithic astronomy into his picture of the society of the megalith-builders.
At Stenness the astronomical theory
implies a connexion between two sites separated chronologically by many centuries.
Indeed much work on megalithic astronomy lumps together struct-
ures which the archaeologist sees no reason for connecting.
One way to
rectify the situation is chosen by Aubrey Burl (see his paper in this volume), who recommends studying the orientation of monuments which can be grouped together on archaeological grounds.
This makes the task of the
archaeologist easier, obviously, but unless archaeologists have said the last word on the connexions between monuments of different types and in different places, it is at least possible that useful evidence will be ignored by such a 'correct1 approach.
The extent to which archaeologically
mixed or uncertain material can contribute is something considered by Dr Ruggles in his paper. Another aspect of megalithic astronomy of importance in the wider context is its purpose.
This can be classified in various ways, for
example, as ritual, practical or scientific, though these terms have no significance which is universally agreed.
But one concept which appears
more and more to find favour is the idea that all the orientations for which the evidence is satisfactory can be understood as ritual orientations of no great precision.
Again this seems a comfortable idea that makes as few de-
mands on us as the construction of such orientations would have done on the megalith-builders.
And yet it may not be quite so simple.
In his paper in
this volume Aubrey Burl draws attention to the orientations of the Clava passage-graves.
Though the data is admittedly provisional, the apparent
existence of orientations to the standstills of the moon implies that observations were made, recorded and recalled over a period of the order of 19
Heggie: Megalithic astronomy: highlights and problems
years.
22
It seems unreasonable to suppose that this was done on the basis
of haphazard or sporadic observations;
rather, there must have been a rel-
atively systematic programme of observations, which no one observer may have lived long enough to complete (Atkinson 1975).
These orientations are
not particularly accurate, but the orientation of the avenue at Stonehenge (see Atkinson's paper in this volume) indicates, in the simpler context of a solstitial sightline, that considerably higher accuracy was attainable and, perhaps, intended.
It is a very small step from here to the solstitial
orientations of high accuracy, such as the north-west foresight viewed from the central stone at Ballochroy.
These have been a feature of Prof. Thorn's
evidence ever since his earliest papers on megalithic astronomy, where, it will be recalled, selection problems were relatively untroublesome.
This
is not to say that such sightlines, if genuine, served a scientific purpose, satisfying the curiosity of the megalithic observers about the motion of the sun.
But they are quite a long way from the picture of 'ritual orient-
ations' which this phrase tends to evoke. It might be hoped that the evidence of ethnoastronomy could shed some light on the meaning of the astronomical orientations that we find.
Aubrey Burl's paper illustrates one of the few contacts which this
discipline has had with megalithic astronomy so far, and there seems little prospect that this will improve.
This state of affairs, and especially
what was seen as the reluctance of European archaeoastronomers to draw on the evidence of ethnoastronomy, was the basis of some mild criticism from the Americans at the Oxford conference.
Perhaps one can understand why,
in the context of much American archaeoastronomy, the absence of any contact with ethnohistorical evidence should be viewed with suspicion, but the immense value of Prof. Thorn's work shows that, in the megalithic context, the sanction of ethnoastronomy should not be seen as mandatory.
In his
paper, Prof. Atkinson reminds us of the wise words of Jacquetta Hawkes, who warned us that our view of Stonehenge is inevitably coloured by the age we live in.
If the Age of Science is followed by an Age of Ethnoastron-
omy, let us hope her words are not forgotten.
NOTES 1. A number of useful comments have been made about that paper. Prof. Atkinson kindly pointed out that the balance of evidence clearly favours the supposition that hole F at Stonehenge is natural (p.S29), and comments by Dr Ritchie and Prof. Thorn have been incorporated within the present text. Also, on p.S32, line 2h 9 for 'Kintraw' read 'Kilmartin'. 2. The page number refers to the Fontana edition (London: 1970),
Heggie: Megalithic astronomy: highlights and problems
23
REFERENCES Atkinson, R.J.C. (1975). Megalithic astronomy - a prehistorian's comments. J. Hist. Astron., 6_, U2-52. Barlai, K. (1980). On the orientation of graves in prehistoric cemeteries. Archaeoastronomy (Bulletin), _3, no.i+, 29~32. Brennan, M. (1980). The Boyne Valley Vision. Portlaoise: Dolmen Press. Burl, H.A.W. (1976). The Stone Circles of the British Isles. New Haven and London: Yale University Press. Burl, H.A.W. & Piper, E. (1979). Rings of Stone. London: Frances Lincoln. Dobrzycki, J. (1963). Astronomiczna interpretacja prehistorycznych zabytk6w na terenie polski. Kwart. Hist. Nauk. Tech., _8, 23-7. Freeman, P.R. (1975). Carnac probabilities corrected. J. Hist. Astron., _6, 219. Freeman, P.R. & Elmore, W. (1979). A test for the significance of astronomical alignments. Archaeoastronomy, _1, S86-S96. Hadingham, E. (l98la). The lunar observatory hypothesis at Carnac: a reconsideration. Antiquity, _5_5, 35-^2. (l98lb). (Book review). Archaeoastronomy (Bulletin), U_9 no.2, kh-5. Hawkins, G.S. (1968). Astro-archaeology. _In Vistas in Astronomy, ed. A. Beer, 10, pp. 1*5-88. Oxford: Pergamon. (1971). Photogrammetric survey of Stonehenge and Callanish. In. National Geographic Society Research Reports (1965 Projects), ed. P.H. Oehser, pp. 101-8. Washington: Nat. Geogr. Soc. (1973). Beyond Stonehenge. London: Hutchinson. Hawkins, G.S. & White, J.B. (1965). Stonehenge Decoded. New York: Doubleday. Heggie, D.C. (l98la). Megalithic Science. London: Thames & Hudson. (l98lb). Highlights and problems of megalithic astronomy. Archaeoastronomy, _3, S17-S37. MacKie, E.W. (197M. Archaeological tests on supposed prehistoric astronomical sites in Scotland. Phil. Trans. R. Soc. Lond. A, 276, 16991. (1977). The Megalith Builders. Oxford: Phaidon. Merritt, R.L. & Thorn, A.S. (1980). Le Grand Menhir Brise*. Archaeol. J., 137, 27-39. Morrison, L.V. (1980). On the analysis of megalithic lunar sightlines in Scotland. Archaeoastronomy, 2_, S65-S77. Muller, R. (1936). Himmelskundliche Ortung auf Nordisch-Germanischem Boden. Leipzig: Curt Kabitzsch. (1970). Der Himmel liber dem Menschen der Steinzeit. Berlin: Springer-Verlag. Patrick, J.D. (1981). A reassessment of the solstitial observatories at Kintraw and Ballochroy. _In Ruggles & Whittle (l98l), pp. 211-19. Roy, J.-R. (198O). Comments on the astronomical alignments at Callanish, Lewis. J. Roy. Astron. Soc. Can., jh_, 1-9. Ruggles, C.L.N. (1981). A critical examination of the megalithic lunar observatories. In Ruggles & Whittle (1981), pp. 153-209. (1983). A reassessment of the high precision megalithic lunar sightlines. Part two: foresights and the problem of selection. Archaeoastronomy, _5_, to appear. Ruggles, C.L.N. & Whittle, A.W.R., eds. (1981). Astronomy and Society in Britain During the Period ^000-1500 B.C. Oxford: Brit. Archaeol. Rep. Thorn, A. (195*0. The solar observatories of megalithic man. J. Brit. Astron. Ass., §k9 396-UOU.
Heggie: Megalithic astronomy: highlights and problems
24
Thorn, A. (1955). A statistical examination of the meaglithic sites in Britain. J. R. Stat. Soc. A, 118, 275-95. (1966). Megalithic astronomy: indications in standing stones. In Vistas in Astronomy, ed. A. Beer, j[, pp. 1-57. Oxford: Pergamon. (1967). Megalithic Sites in Britain. Oxford: Clarendon Press. (1969). The lunar observatories of megalithic man. In Vistas in Astronomy, ed. A. Beer, 11, pp. 1-29. Oxford: Pergamon. (1971). Megalithic Lunar Observatories. Oxford: Clarendon Press. Thorn, A. & Thorn, A.S. (1978a). Megalithic Remains in Britain and Brittany. Oxford: Clarendon Press. (1978b). A reconsideration of the lunar sites in Britain. J. Hist. Astron., £, 170-9. Thorn, A.S. (1981). Megalithic lunar observatories: an assessment of U2 lunar alignments. In Ruggles & Whittle (1981), pp. 13~6l.
25
ARCHAEOLOGY AND ASTRONOMY:
AN ARCHAEOLOGICAL VIEW
J. N. Graham Ritchie Royal
Commission
on
the
Ancient and Historical
Monuments
of Scotland
Abstract. This paper examines some of the problems of the archaeological evidence from sites for which astronomical interpretations have been proposed; these include problems of interpretation caused by the use of many prehistoric sites over a long period of time, and difficulties raised by the absence of a firm chronological frame-work. The absence of detailed gazetteers for many of the types of site under discussion is also stressed. A number of excavations are used to contrast the material available to the prehistorian and to the astronomer. Introduction The astronomical interpretation of stone circles and standing stones has a long history;
in the late seventeenth century, for example,
Martin Martin, writing about the Ring of Brodgar and the Stones of Stenness in Orkney, records that
'Several of the Inhabitants have a
Tradition that the Sun was worshipped in the larger, and the Moon in the lesser Circle1
(1716, 365).
In recent years a scientific basis
for interpretation of the archaeological evidence in astronomical terms has been proposed by Alexander Thorn (Thorn, A. 1967; 1978).
1971;
Thorn & Thorn
In 1965 he began his introduction to megalithic astronomy:
•Much has been written for and against the astronomical significance of the stone circles, stone alignments, etc., which are scattered throughout these islands and indeed much further afield. universal
There is, however,
agreement that the erectors, herein called for convenience
Megalithic man, marked the rising and setting points of the solsticial Sun' (Thorn, A. 1965, 1 ) . proposed,
In more recent books and papers he has also
amid greater controversy, a series of lunar observatories.
The present introduction was designed as a conference paper offering both a personal assessment of the range of sites for which astronomical interpretations have been proposed, and as a background detailed papers that follow.
to the more
As delivered, it was intended to provide
both a visual evocation of the range of material available and also
Ritchie:
An Archaeological View
26
a body of evidence from which a number of general points about our understanding of the sites might be made. scene, man
1
a broadly
In setting the archaeological
chronological approach to the works of
'Megalithic
in Britain, highlighting some of the fundamental problems and the
inadequacies of the archaeological evidence, may be useful. The structural use of large stones, particularly in northern and western parts of the country, occurs at many stages in man's past; thus we should no longer envisage any unity of megalithic or 'tradition' nor think in terms of 'Megalithic man'.
'culture'
Such a figure
was easier to imagine at a time when the neolithic and bronze ages in Britain were thought to span a millennium and a half;
but we now know
that the monuments span a period of about four millennia, and complex relationships and the existence of independent traditions are altogether more likely.
The use of timber for monumental structures in southern
and eastern parts of Britain is too readily overlooked if we are bemused by the megalithic label. Some of the earliest sites are the burial monuments known as chambered tombs, built and used as collective burial-places for as long as a millennium and a half, from 4000 BC to 2500 BC in broad terms and in calibrated dates.
Earthwork circles, some containing rings of
standing stones or upright timbers, known as henge monuments, may belong, again in very broad terms, to the millennium spanning 3500 BC to 2500 BC;
such henge monuments are presumably religious or ceremonial centres
for communities from the surrounding neighbourhood. alignments,
single
standing
stones
and
round
Stone circles, stone
cairns with monumental
kerbs are rather more difficult to date, but they form the bulk of the monuments
for
which
astronomical
interpretations
have
been
claimed.
Our vision of past societies depends, of course, not only on the evidence of burial and ritual monuments, but also on that from settlement sites, pottery 1979;
and
environmental
data
(see, for example, Megaw and Simpson
Burgess 1980). Chambered tombs The structural evidence itself is not always easy to interpret
and excavation often reveals that more than one building period may be involved;
many centuries after the initial construction of a site,
burials or ritual deposits may be inserted, attracted by the numinous aura of impressive upright stones. prehistoric
The multi-period nature of many
monuments may be illustrated initially by two very different
Ritchie:
chambered
tombs:
in Argyll. with
a
burials
An Archaeological View
Wayland's
Smithy
27
in Oxfordshire
and Achnacreebeag
At Wayland's Smithy the primary structure was a small mound
complex (the
mortuary
skeletons
enclosure in part
containing
at
least
in
partially
articulated
anatomical
order) and
associated with two massive pits, which had formerly held substantial split tree-trunks.
Later, but perhaps not much later, the small mound
was buried
a much
beneath
larger
one
associated
with
transepted megalithic tomb at a date of about 3500 BC.
a
monumental
At Wayland's
Smithy, the sequence is shown stratigraphically, one phase being sealed by another (Atkinson
1965).
At Achnacreebeag, two upstanding megalithic
structures were clearly visible before excavation and the question was: were they contemporary and if not, which was the earlier?
The answer,
that the simpler structure was the earlier, and the small passage-grave a later addition, was arrived at by the careful examination and planning of the stones of the cairn, showing that the cairn enclosing the passagegrave had been built at a later date on to one side of an existing round cairn
(Ritchie 1970).
between structures
This type of rather more oblique relationship
is a constant feature of the excavation of stone
circles and is one that makes the working out of any sequence rather more subjective, even on excavated sites. Can
the
Achnacreebeag
sequence
be
extrapolated
to
the
unexcavated chambered tomb of Greadal Fhinn, situated near the tip of the Ardnamurchan peninsula in Argyll, where very similar structural remains survive?
Only excavation will tell;
sadly, however, this site is still
included as a stone circle on many distribution maps, probably because of its description as such on early Ordnance Survey maps, but there is no doubt that it is a passage-grave within a round cairn (Henshall 1972, 358-60).
This example may be used to stress the absence of reliable
descriptive gazetteers for many of the types of site under discussion, except for chambered tombs themselves (in Scotland, for example, Henshall 1963 & 1972).
There are many lists of sites, but we lack gazetteers
for stone circles, alignments or cairns with detailed descriptions and plans, and thus we lack a firm archaeological data-base in published form, though there are of course good local or general studies (notably Burl a
1976).
site
All too frequently
astronomers and archaeologists
under different names and locate them
in different ways
latitude and longitude or by National Grid Reference).
list (by
Only rarely
in the astronomical literature is there cross reference to archaeological
Ritchie:
An Archaeological View
28
discussion - excavation reports, Royal Commission Inventories or Ordnance Survey Record Cards for example;
thus there may be no account taken
of the past history of the site including the movement or re-arrangement of stones.
This is important because stone structures of many
types in a collapsed or ruined state may superficially resemble circles' or 'stone alignments'. may be cited:
'stone
One illustration of this sort of problem
The Eleven Shearers, Roxburghshire, described by Thorn
as an alignment (1967, 149) is included in the Commission's Inventory (£ace_ MacKie
1975, 78-9) 1
(RCAMS 1956, 194, no. 409), although such contrasting
ancient field-dyke interpretations horizon-plots
are
for
'as nothing more than the grounders of an
clearly
most
a
matter
of opinion.
We lack complete
sites to compare with the selected
fragments
that are thought to be astronomically significant. Chambered tombs have indeed found their way into astronomical discussions, Unival and Clettraval in North Uist, for example, although the original nature of the tombs as burial places was not necessarily recognised (for the archaeological interpretations see Moir 1980; Ruggles & as
Norris 1980;
Atkinson 1981, 206*, Ruggles 1981, 164).
a group, chambered
But studied
tombs do not appear to have connections with
astronomical happenings, with a few important exceptions.
The monumental
cruciform passage-grave at Newgrange, in County Meath, is of interest both
because
it
is
surrounded
by
a
stone
circle
and
because
the
orientation of the passage permits the light of the midwinter rising sun to illuminate
the end recess of the chamber
opening above the passage - the
'roof box'
through an unusual
(Patrick 1974).
If the
surrounding stone circle is indeed an integral part of the original plan, a date of about 3300 BC may be put forward for it on the evidence of the radiocarbon dates, and it is thus among the earliest stone circles known at present. of British
At Maes Howe, in Orkney, one of the most magnificent
passage-graves, a clear interest in celestial events may
also be seen in the orientation of the entrance passage, for the rays of the setting sun illumine the rear wall of the central chamber at the time of midwinter sunset.
The fact that the stone that blocked
the passage is not quite tall enough to fit to the top of the entrance has also been brought into the discussion, and Welfare and Fairley
suggest
that this was to allow a shaft of light to penetrate the chamber even when the entrance was sealed (1980, 93).
Ritchie:
29
An Archaeological View
The Stones of Stenness and the Ring of Brodgar Recent excavations have shown that the use of the Maes Howe class of tomb in Orkney is broadly contemporary with that of the stone circle and henge monument of the Stones of Stenness - that is at a date early in the third millennium BC. graphical
relationships
apparent;
between
At Stenness, the absence of stratithe
various
structural
elements
is
pits A-E for example are probably as late as AD 500 or so
as a result of a radiocarbon determination from one of them (ad 519 + 150
SRR-352 ); (Ritchie 1976, 15).
The circle is surrounded by the
ditch and bank of the henge, but it seems likely that they and the rectangular
stone
setting
at
the
centre
of
the
site
are
broadly
contemporary - the evidence being provided more by symmetry than anything else.
Pottery from the bottom of the ditch and from within the central
setting is comparable to material from the chambered tomb of Quanterness, 11 km to the E, excavated by Colin Renfrew (1979).
As there are also
similar radiocarbon dates from Quanterness we may be justified in making the
chronological
equation
between
the
use of Stenness and that of
Quanterness, and thus we know something of the burial places and of the
'ceremonial' centres, be they for religious or secular activities
within the community.
Similar radiocarbon dates and pottery within
F ig. 1. Stones of Stenness, Orkney: plan of structures at the centre of the circle, square stone setting with the position of a possible timber upright, sockets with packing stones from which uprights have been removed, and remains of possible timber setting (Ritchie 1976, fig. 4 ) .
PLAN OF CENTRAL FEATURED ''7™'^?^
natural
N-S SECTION OF 5AME AREA
Ritchie:
An Archaeological View
30
the same broad typological class known as 'grooved ware1 found at the settlement sites of Skara Brae and Rinyo shows that we can appreciate the economic position of the users of such monuments more precisely than perhaps anywhere else in Britain (see Clarke 1976 a and b ) .
An
example of the sort of re-organisation that may take place within stone circles is illustrated by the setting to the north of the centre of the site (Fig. 1), where two sockets dug to receive upright stones were found;
the stones had been removed, but some of the original packing
was still in position.
The stones seem to have been associated with
a square timber setting, but sadly there is no helpful indication of the It
date is
of
the
surprising
original
construction
or
their
perhaps that no astronomical
deliberate removal.
significance has ever
been postulated for what may have been an upright post within the central stone setting at Stenness
(Ritchie
1976, 12-13);
do we see here a
gnomon for the observation of shadows cast by the sun or is this a preliminary marker
in the observation of the perturbation wobble of
the moon (Thorn,A. S. 1981, 57)? The area round the Ring of Brodgar (Fig. 2 ) , situated km
to
the
NW, has several suggested
Fig. 2.
1.5
astronomical alignments, making
Ring of Brodgar, Orkney.
Ritchie:
An Archaeological View
31
use particularly of the burial mounds around the henge and stone circle. Recent
excavation
by
Colin Renfrew has been confined
to examination
of the ditch and possible bank, and the radiocarbon dates obtained do little more than indicate that the ditch would still have been a conspicuous feature in the second half of the first millennium BC (Renfrew 1979, 39-43).
It is worth stressing that the Stenness dates should
not be used to indicate the period of use of the Ring of Brodgar, sister monuments though they appear to be
(Thorn, A. S. 1981,42-3), for the
dates obtained for various henge monuments in Britain cover a wide chronological span.
But it is not at all impossible on archaeological grounds
that the barrows round Brodgar are broadly of the date put forward by Alexander and A. S. Thorn for the use of the site as a lunar observatory - that is between about 1600 BC and 1400 BC (Thorn & Thorn 1973; 1978, 122-37).
1975;
On the other hand it is wrong to imply that structures
can be 'dated by archaeoastronomy' (Baitey 1973, 399);
only a possible
period of use of a stone or circle can be so indicated. This discussion of the Ring of Brodgar tellingly illustrates an
important
difference
between
the
sort
and astronomers have at their disposal.
of evidence
archaeologists
The relevant positions of all
lunar standstills from 2088 BC to 1307 BC as calculated from figures provided by the Royal Greenwich Observatory round the Ring can be plotted
for the various sightlines
(Thorn & Thorn 1975, 100, fig. 7 ) .
This
reflects the rather more precise nature of the astronomical information - available
in chart form, susceptible of comparative precision even
when translated into past ages and various latitudes.
This is in stark
contrast to the silent stones of the archeological landscape, at periods when there are no written records at all. on
such
astronomical
Examination of the literature
matters will show that many archaeologists use
the basis of their own excavations and survey to build up a body of evidence, about which in their own minds they are reasonably certain, and this policy has deliberately been continued, at least in part, in this
introduction.
personal
than
Archaeological
astronomical
ones
statements
and
are
based
pretations of what is acceptable evidence; to
disprove
the
astronomical
potential
thus
of
on
seem
to be more
individual inter-
it is very rarely possibly any
site
on astronomical
grounds, and it is more often the validity of the archaeological evidence that
is
ancient
in man
contention. is
likely
The more philosophical to have
used
question of whether
standing stones as markers for
Ritchie:
32
An Archaeological View
astronomical observation is not one that is possible to answer at all, except perhaps from
a statistical point of view, using both archaeo-
logical and astronomical observations that are acceptable to all.
It
is interesting that evidence for the use of features of the horizon as foresights for the detailed observation of the moon does not seem to be forthcoming from other societies in northern latitudes. Standing Stones Single
standing
stones
occur
widely
throughout
northern
and western Britain, sometimes isolated and remote, sometimes in apparent association with other groups of site such as cairns or cists;
nor
are all standing stones of prehistoric date, as some have been set up
Fig. 3. Try, Gulval, Cornwall: A, plan and section of standing stone, cist and cairn. a, medium brown soft soil; b, dark brown soft soil filling the socket from the menhir; d, chocolate-brown weathered c, grey leached gritty soil; rab; e, rab upcast of the pit dug to receive the cist; B, beaker from the cist (scale 1:3) (after Russell and Pool 1964, 17, fig. 5 and 19, fig, 6, no. 7 ) .
. ..•'lU'WlM,,,,,^''',,,
• ",
Ritchie:
33
An Archaeological View
in comparatively recent times as route- or boundary-markers, scratching posts for cattle, or indeed fence posts (as noted in Kansas by Myres 1965).
Only when there is evidence from within the backfilling of the
hole or socket that was dug into the ground to receive them, or stratigraphical
information about their sequence within a complex monument
is it possible to suggest a date for their construction.
Until recent
times it was only in remarkable cases that it was possible to be sure of the date of the removal or destruction of a stone, as for example the
'Barber's Stone1
at Avebury, felled about AD 1320-5 accidentally
trapping an unfortunate barber-surgeon beneath it, or Odin's Stone in Orkney broken up amid local consternation in December 1814. Excavations of standing stones include that at Try, Gulval, in Cornwall
(Fig. 3 ) , for example, where beside a monolith there was
a cairn of stones, which covered a cist containing a burial associated with a beaker vessel (Russell and Poole 1964).
The excavators describe,
however, that the upcast soil from the pit dug for the cist partly overlay the soil filling of the socket of the upright, and thus the stone is the earlier feature;
the absence of any silting or weathering layer
suggested that there was only a short interval between the two operations.
Fig. 4.
Maol Mor, Dervaig, Mull, Argyll:
standing stones.
Ritchie:
An Archaeological View
34
The handled beaker thus provides an approximate date for the erection of the menhir within the suggested chronology for such vessels at the time of any discussion, currently about the 18th to 17th century BC. An independent chronology provided by radiocarbon analysis, had suitable material existed, would of course be rather more satisfactory, and unlike typology, less susceptible to changes of archaeological fashion. Many dating
of
of
the
alignments
interpretation
same
archaeological
of standing
in astronomical
problems
occur over the
stones, though their potential for
terms is much greater;
an example of
a linear setting of stones from Mull illustrates this class of site (Fig.
4) - Maol Mor, Dervaig
(Thorn's Dervaig A ) .
Excavation of the
sockets of menhir and stone alignments have in fact done little more than
stress
a function related
to burial or activities for which a
dedicatory deposit of human cremated bone was appropriate.
In primary
association with the erection of one of the stones of the Ballymeanoch alignment, in Argyll, there were distinct deposits of bone against the NE and SE faces of the stone (5 gm in each), with a larger deposit of 90 gm on the SW side near the base of the socket (Barber 7).
1978, 106-
Within the socket of a pair of stones at Orwell, Kinross-shire,
a double cremation deposit separated by a flat slab was probably part of the ceremonial at the time of the erection of the stone and the backfilling of the socket;
the presence of burnt dog and pig bones with
the lower cremation deposit may be thought to provide an of the original rituals of cremation.
impression
In the nineteenth century further
cremation patches and cists were found round the stones (Ritchie 1974, 8-9).
A date for some of these activities may be suggested by the excav-
ation at Pitnacree, Perthshire, where at the top of the mound there was a standing stone, at the base of which there was a scattered cremation and a large amount of carbonised wood; date of
this provided a radiocarbon
2270 be + 90 (GaK-602) (Coles & Simpson 1965, 38). The presence
of burials
associated
with food vessels and cinerary urns indicates
that the use of standing stones in this focal way may have continued into the mid-second millennium BC and beyond (Burgess 1980, 345-6), and this may have a bearing on their postulated use as astronomical markers. At Duntreath (or Blanefield) ,in Stirlingshire, the excavation was undertaken to examine the likelihood of the use of stones in an astronomical way (MacKie 1973; which
1974, 187); Euan MacKie found a layer of ash and charcoal
suggested
fires
associated with the stones and which provided
Ritchie:
35
An Archaeological View
a radiocarbon date of 2860 be + 270 (GX-2781), although MacKie stresses that this was not conclusive be echoed;
(1977, 118).
MacKie's final caution may
Duntreath illustrates the dangers of assuming that all the
problems are solved simply because none are apparent in the small quantity of hard evidence available
(1974, 187).
Excavations such as Orwell
and Duntreath are not perhaps exciting in themselves, but in the short term they illustrate the sort of small-scale work that is needed to build up a positive body of evidence about the dates and associations of far more stones;
in the long term, however, only more extensive
work, as at Rhos-y-clegyrn, Pembrokeshire, will put such sites in a proper context (Lewis 1974). Stone Circles (Fig. 5) The excavation of a stone circle may also raise problems of stratigraphy and the relationship of the various pieces of evidence, not
least
because
it
is difficult to know when a feature within a
a stone circle relates to an early phase of its construction or whether it is a later addition - like the pits from the Stones of Stenness mentioned earlier.
We may suppose, from the symmetry of the deposition,
that the cinerary urn from Sandy Road, Scone, in Perthshire, is broadly contemporary with the setting up of the circle and that the radiocarbon
Fig. 5.
Lochbuie, Mull, Argyll:
stone circle.
Ritchie:
An Archaeological View
date of 1200 be + 150
36
(GaK-787) from charcoal within the urn refers
to the construction of the site itself, but this is little more than an assumption, and the central position would also be a favoured one for later depositions (Stewart 1966). This demonstration of the problematic nature of the archaeological evidence does not disguise the fact that much of the material at our disposal has a wide chronological span, certainly from 3000 BC at least the middle of the second millennium BC.
to
Ruggles has illustrated
the variation in the setting lines for the Moon's upper and lower limbs over the period 2500 BC to 1500 BC at Ballinaby, Islay (1981b, 753; compare
Thorn
& Thorn 1978, 170, fig. 13.1). This sort of exercise undermines confidence in the lunar lines proposed by the Thorns when one considers that on archaeological
grounds
the
sites
must
range
(possibly
randomly
and
possibly with concentrations) from Stenness early in the third millennium BC (on the evidence of the radiocarbon dates) perhaps to Fowlis Wester in the middle of the second millennium BC (an archaeological estimation) (Atkinson 1979, 101).
The poster paper presented by the writer to
the conference took up the theme of site interpretation;
this is of
paramount importance in providing a clear account of the archaeological background.
Stone circles, single standing stones and burial cairns
belong to distinctive categories of monument in some cases constructed at different dates for different purposes, and in other cases forming what appear to be small associated groups.
Thus when used together
to provide a series of sites for which similar astronomical functions are proposed, the archaeologist is bound to feel uneasy (Fleming 1975). In
an
interesting
exercise
comparing
the
astronomical potential of
two structurally similar sites, Temple Wood and Barbreck in Argyll, Jon Patrick found that no similarities in astronomical use could be postulated for the latter (1979), and this may be thought to cast doubt about the lines observed at the former (Heggie 1981b, 186). Stone
circles themselves can be broken down into several
classes both on typological and geographical grounds; 'entrance-circles' Ireland, the
of
Cumbria,
the
'recumbent
including the
stone-circles'
'four-posters' of Perthshire and NE Scotland
of
SW
(with some
outliers), but perhaps the best known being the 'recumbent stone-circles' of NE Scotland, recently studied
in detail by Aubrey Burl, including
an examination of their archaeoastronomical potential
(1980).
In the
past our understanding of the various groups has been bedevilled by the fact that many stone circles proved a magnet for nineteenth century
Ritchie:
An Archaeological View
37
antiquaries with indiscriminate excavation methods, and though we may know what was discovered than certain. at
Loanhead
in them, the various relationships are less
In the north, the excavations of Howard Kilbride-Jones of Daviot and Cullerlie helped to change the format of
reporting, but sadly Loanhead was already severely
disturbed
(1935).
After the War the excavations of Stuart Piggott at Cairnpapple, the Clava sites, and latterly at Croft Moraig significantly increased our knowledge;
at the latter site the interesting sequence from
timber monument to stone circle was demonstrated (Piggott and Simpson 1971).
Stuart Piggott has recorded the visit of Ludovic Mann, the veteran
Scottish antiquary, to Cairnpapple in 1948;
Mann's only words on seeing
the plan of the stone holes of the henge were 'It's an egg, Professor, and that's the beginning of a new era!'
Today such a view would no
longer be thought altogether eccentric, as Alexander Thorn has convincingly shown that stones were deliberately set out in several geometric shapes: the flattened circle, the ellipse, the egg, and the complex circle probably using a standard unit of length the & Thorn
'Megalithic Yard' (Thorn
1978, 18, fig. 3.1). Cairns
(Figs. 6 & 7)
One distinct class of cairn is of particular interest to those working on astronomical interpretations because examples include cairn B at Kintraw, the cairns at Monzie, Ballymeanoch and one of pair of sites at Fowlis Wester.
the
The excavation of the small cairn at
Strontoiller in Argyll (Thorn's site Loch Nell Al/2) showed that large erratic boulders formed the contiguous kerb-stones of a low cairn, with a fragmentary cremation burial in the lowest levels;
scatters of white
quartz pebbles were found round the kerb stones (Ritchie 1971). cairns
are
clearly
closely
Strontoiller and Temple Wood;
related
to
stone
ated
with
single
at
Kerb
Lochbuie,
to linear settings of standing stones
at Ballymeanoch and at Ardnacross, on Mull;
Strontoiller and Achacha.'
circles
outlying
standing
Astronomical
and they are often associstones,
for
example
at
inferences have been drawn for
some, though not all, the examples of this class, frequently in the past described as stone circles, though this can no longer be an accurate label;
echoing Aubrey Burl's recent plea for the study of groups of
monuments, it would be instructive to see if from an astronomical point of view a consistent use is forthcoming for this class as a whole.
Kerb
cairns as a group may be related to the recumbent stone circles of NE
Ritchie:
An Archaeological View
Fig. 6. Ardnacross, Mull:
standing stone and cairns.
Fig. 7. Strontoiller, Argyll:
.•*
# cremation ••«• auartz chips #M& disturbed
VIAN SECTION
38
kerb cairn.
Ritchie:
An Archaeological View
39
Scotland and to the ring-cairn tradition, but the nature of such crosscountry
contacts
is
impossible
to determine archaeologically, though
very similar cairns are found in the north-east - perhaps most remarkably at Cullerlie.
Some
indication
of
the
date
of
the kerb-cairn class
is provided by the excavations at Claggan, Morvern, Argyll, where there are two radiocarbon determinations from charcoal associated with cremations:
975 be + 50 (SRR-284) and 1058 be + 40 (SRR-285) indicating
a date around 1200 to 1300 BC in corrected terms (Ritchie et al. 1975). Conclusions The deliberately
problems
stressed
of
archaeological
interpretation
have
been
for several reasons - one is that the archaeo-
logical evidence at present formulated, at least in terms of published, material, cannot provide the firm basis for the sort of examination that is so clearly needed for an independent evaluation of the astronomical
hypotheses.
Secondly, the chronological
span of stone circles
and cairns (which are more susceptible to modern dating techniques than single standing stones or alignments) means that a greater appreciation of
the
various
typological and chronological groups
is essential
if
the astronomical possibilities are to be slotted into a broad pattern. The position and orientation of many of the sites
had almost certainly
been established by 1700 BC to 1500 BC, by the time that the more precise astronomical observations are postulated. Douglas
Heggie posed an important question in his intro-
ductory paper to the conference:
must unexcavated sites be excluded
from astronomical consideration until they have been excavated? 29). said
The archaeological purist might say to
underline
the
uncertainties
of
(1981a,
'yes1, and enough has been
the archaeological evidence,
but this is not altogether a practical answer in view of the small number of sites that will in fact be excavated even by the end of the century; there may, however, be grades of uncertainty.
The superficially most
complex sites (chambered tombs and stone circles) were probably in use, and being constructed over a long period of time, and in an unexcavated state may show merely the surviving features of the final stage of building or use.
Rather simpler sites (linear setting of stones and cairns)
are not as liable to change shape radically on excavation, and may be more helpful even in a raw state, though their chronological position will
remain
uncertain.
It
is
from
an interpretation of the field
evidence that is accepted by all within an agreed chronological frame-
Ritchie:
An Archaeological View
40
work (despite all the problems that this raises for the archaeologist) that the subject must proceed present parallel paths.
(Ritchie 1980, 98) rather than on its
In his discussion of future development Heggie
stresses the importance of a rigorous attention to a statistical approach (1981a, 34;
1981b) and it is likely that only with joint programmes will
the subject be taken forward:
archaeological responsibility for site-
interpretation, classification and possible chronological niche;
site-
survey and horizon-plotting to the highest standards within an archaeological
and
astronomical
framework;
statistical
evaluation of the
groups of sites with potential astronomical indicators. would also lead
to
the
publication
of
detailed
Such a process
site-gazetteers
the
absence of which so hampers further research. Alexander Thorn's work has made many prehistorians re-assess their views on the likely achievements of early societies in theoretical fields;
the architectural or structural achievements can be appreciated
in the field (stone circles, or chambered tombs), the high standard of craftmanship be it in pottery or metalwork is obvious, but the role of
'science'
in society
is difficult to assess.
Thorn's work has,
however, had an important effect on the ways in which we evaluate our material, whether in wide-ranging theoretical constructs or in a more traditional approach to the society of prehistoric man (Baitey 1973, 415-16;
MacKie 1977;
Ellegard
1981;
Heggie 1981b).
The careful
surveys by Alexander Thorn have also been a spur to more meticulous work
in
archaeological
appearing (Burl 1980;
recording,
the
fruits
of
which
are already
Ruggles 1981a), but the rough north points of
many published archaeological plans mean that the sites will have to be
re-surveyed
before
their
astronomical
assessed (see also Baitey 1973, 400).
potential
can be properly
The method of presentation both
of negative evidence and of horizon plots that have proved to be without astronomical significance may also have to be reconsidered; the reaction of Owen Gingerich, an astronomer, to Thorn's hypotheses, following his own field-examination of the sites, as 'pyschologically devastating' to a tentative acceptance of precision astronomy (in Elleg&rd 1981, 117) is particularly telling.
in ancient Britain
Thus if to the present
writer a not proven verdict remains over the question of detailed astronomical observation in prehistoric times, this does nothing to diminish Alexander
Thorn's
contribution
to
our
approach
to
past
societies.
Ritchie:
An Archaeological View
41
Acknowledgements and copyright of illustrations The writer is indebted to the following for assistance during the preparation of this paper:
Anna Ritchie, John Barber, D. C. Heggie,
Linda Louden, Stuart Piggott, A. MacLaren, I. G. Scott, J. G. Scott, J. N. Stevenson, and the photographic staff of the Commission. The figures are Crown Copyright, Royal Commission on Ancient Monuments, Scotland with the following exceptions:
Fig. 2.
Crown Copy-
right, Scottish Development Department (Ancient Monuments), under whose auspices the excavations at the Stones of Stenness (Fig. 1) were undertaken;
Fig. 3A, re-drawn with kind permission Miss V. Russell and P.
A. S. Pool ; Fig 3B after Russell and Pool 1964, fig. 6, no. 7. References Atkinson, R. J. C. (1965).
Thorn 1978). Atkinson, R.
J. C.
Wayland's Smithy, Antiquity, 39, 126-33.
(1979).
Atkinson, R. J. C.
The Thorns' new book (review of Thorn and
Archaeoastronomy, 1, 99-102.
(1981).
Comments on the archaeological status of
some of the sites. Baitey, E.
(1973).
C.
In Ruggles and Whittle 1981, 206-9.
Archaeoastronomy
and
ethnoastronomy
so far.
Current Anthropology, 14, 389-449. Barber, J. W. (1978).
The excavation of the holed-stone at Ballymeanoch,
Kilmartin, Argyll, Proc. Soc. Antiq. Scot., 109, 104-11. Burgess, C. (1980). Burl, A. (1976).
The Age of Stonehenge.
Dent.
The Stone Circles of the British Isles.
and London: Burl, A. (1980).
London:
New Haven
Yale University Press.
Science or symbolism:
problems of archaeoastronomy.
Antiquity, 54, 191-200. Coles, J. M. & Simpson D. D. A. (1965). round
barrow
at
Pitnacree,
The excavation of a neolithic Perthshire,
Scotland.
Proc.
Prehist. S o c , 31, 34-57. Clarke, D. V.
(1976a).
The neolithic village at Skara Brae, Orkney:
1972-73 excavations: Clarke, D. V. (1976b).
an interim report.
Edinburgh: H.M.S.O.
Excavations at Skara Brae:
a summary account.
In Settlement and Economy in the Third and Second Millennia B.C. eds.
C. Burgess and R. Miket pp. 233-50.
Oxford:
British Archaeological Reports, British Series no. 33. Ellegard, A. (1981).
Stone age science in Britain?
Current Anthropology,
22, no. 2, 99-125. Fleming,
A.
(1975).
Megalithic
astronomy:
a
prehistorian's view.
Ritchie:
An Archaeological View
42
Nature, 255, 575. Heggie, D. C. (1981a).
Highlights and problems of megalithic astronomy.
Archaeoastronomy, 3, 17-37. Heggie, D. C. (1981b).
Megalithic Science.
Henshall,A. S. (1963 & 1972).
London:
Thames and Hudson.
The Chambered Tombs of Scotland. Edinburgh:
Edinburgh University Press. Kilbride-Jones, H. E. (1935). circle of
at
Loanhead
An account of the excavation of the stone of Daviot and of the standing stones
Cullerlie, Echt, both
HM Office of Works. Lewis, J. M. (1974).
in Aberdeenshire,
on behalf of
Proc. Soc. Antiq. Scot., 69, 168-223.
Excavations at Rhos-y-clegryn prehistoric site,
St Nicholas, Pembs. MacKie, E. W. (1*973).
Archaeol. Cambrensis, 123, 13-42.
The standing stones at Duntreath.
Current Arch-
aeology, 2, no. 5, 279-83. MacKie,
E. W.
(1974).
Archaeological
tests on supposed prehistoric
astronomical sites in Scotland.
Phil. Trans. R. Soc. Lond.,
A. 276, 169-194. MacKie, E. W.
(1975).
Scotland:
An Archaeological Guide.
London:
Faber and Faber. MacKie, E. W.
(1977).
London: Martin, M. (1716). London:
Science and Society
A Description of the Western Islands of Scotland. Bell.
Reprinted 1970, Edinburgh:
Megaw, J. V. S. & Simpson, D. D. A. (1979). Prehistory. Moir,
G.
(1980). Part I.
in Prehistoric Britain.
Elek.
Leicester:
Megalithic
Mercat Press.
Introduction to British
Leicester University Press.
science and some Scottish site plans:
Antiquity, 54, 37-40.
Myres, M. T. (1965).
Standing field stones in Kansas.
Antiquity, 39,
136-7. Patrick, J.
(1974).
Midwinter surise at Newgrange.
Nature, 249, 517-
19. Patrick, J. (1979).
A re-assessment of the lunar observatory hypothesis
for the Kilmartin Stones.
Archaeoastronomy, .1, 78-85.
Piggott, S. & Simpson D. D. A. (1971).
Excavations of a stone circle
at Croft Moraig, Perthshire, Scotland.
Proc. Prehist. S o c ,
37, 1-15. R.C.A.M.S.
(1956).
Royal
Monuments
of
Commission
Scotland.
on
the
Ancient
An Inventory
and Historical
of the Ancient
Ritchie: and
An Archaeological View
Historical
43
Monuments
of
Roxburghshire.
Commission
on
the
Edinburgh:
H.M.S.O. R.C.A.M.S.
(1980).
Royal
Monuments of Scotland.
Argyll:
Ancient
and Historical
an Inventory of the Ancient
Monuments, 3, Mull, Tiree, Coll and Northern Argyll. Edinburgh: Renfrew, C.
(1979).
H.M.S.O. Investigations on Orkney.
London:
Society of
Antiquaries of London, Report of the Research Committee, no. 38* Ritchie, J. N. G. (1970).
Excavation of the Chambered Cairn at
Achnacreebeag. Ritchie, J. N. G. (1971). Argyll.
Proc. Soc. Antiq. Scot. 102, 31-55• Excavation of a cairn at Strontoiller, Lorn,
Glasgow Archaeol. J., 2, 1-7.
Ritchie, J. N. G.
(1974).
Excavation of the stone circle and cairn
at Balbirnie, Fife. Ritchie, J. N. G. (1976).
Archaeol. J., 131, 1-32.
The Stones of Stenness, Orkney.
Proc. Soc.
Antiq. Scot., 107, 1-60. Ritchie, J. N. G. (1980).
Review of Thorn and Thorn 1978.
J. British
Archaeol. Ass., 133, 97-8. Ritchie, J. N. G. et al. (1975).
Ruggles, C.
Small cairns in Argyll:
some recent
Proc. Soc. Antiq. Scot., 106, 14-38.
work.
(1981a).
A critical examination of the megalithic
observatories. Ruggles, C. (1981b)
lunar
In Ruggles and Whittle 1981, 153-209.
Prehistoric astronomy:
how far did it go?
New
Scientist, 90, 750-3. Ruggles, C. L. N. & Norris, R. P. (1980). Scottish site plans:
Part II.
Megalithic science and some Antiquity, 54, 40-3.
Ruggles, C. L. N. & Whittle, A. W. R. eds. (1981).
Astronomy and Society
in Britain during the Period 4000-1500 B.C.
Oxford:
British
Archaeological Reports, British Series no. 88. Russell, V. & Pool P. A. S. , (1964). Gulval.
Excavation of a menhir at Try,
Cornish Archaeol., 3, 1964, 15-26.
Stewart, M. E. C. (1966).
Excavation of a circle of standing stones
at Sandy Road, Scone, Perthshire.
Trans. & Proc. Perthshire
Soc. Nat. Sci., 1^, 7-23. Thorn, A. (1965).
Megalithic astronomy:
indications in standing stones.
In Vistas in Astronomy, 7, ed. A. Beer, pp. 1-57.
Oxford:
Pergamon Press. Thorn,
A.
(1967).
Megalithic
University Press.
Sites
in
Britain.
Oxford:
Oxford
Ritchie:
Thorn, A.
(1971).
An Archaeological View
Megalithic
44
Lunar Observatories.
Oxford:
Oxford
University Press. Thorn,A. & Thorn, A. S. (1973).
A megalithic lunar observatory in Orkney:
the Ring of Brogar
and its cairns.
J. Hist. Astronomy,
4, 111-23. Thorn, A. & Thorn, A. S. (1975). observatory.
Further work on the Brogar lunar
J. Hist. Astronomy, 6, 100-14.
Thorn, A. & Thorn, A. S. (1978). Megalithic Remains in Britain and Brittany Oxford: Thorn, A. S.
(1981).
Clarendon Press. Megalithic
lunar observatories:
of 42 lunar alignments.
an assessment
In Ruggles and Whittle 1981, 13-
61. Welfare, S. & Fairley, J. London:
(1980).
Collins.
Arthur C. Clarke's Mysterious World.
45
THE STATISTICAL APPROACH
P.R. Freeman Department of Mathematics, University of Leicester, LEI 7RH, England
Abstract. A brief summary is given of the need for a statistical approach to assessing most archaeoastronomical data and theories. The various ways in which selection biasses can lead to misleading conclusions, or at least seriously diminish the value of observed data, are described and a few possible techniques for making allowances for them are suggested. A set of three idealistic rules is stated in the hope of improving future observational work. Finally a brief analysis is made of a particular set of data that satisfies nearly all the requirements for lack of bias.
The subject of statistics has, on the whole, a pretty bad public image. Even among scientists it is usually regarded as a necessary evil, a hoop through which one's data must jump before getting accepted for publication. Archaeoastronomers don't even seem to have got this far, since most papers and talks at conferences seem oblivious of the need for taking any kind of statistical view of the data presented. I very much hope that two recent excellent works (Heggie 1981 a,b) will rapidly change this attitude and I strongly recommend all readers of this article to consult both these references. They make nearly all the points that I should have wished to make, so I need not repeat them here. We do not need statistics to help assess the evidence for midsummer sunrise at Stonehenge or midwinter sunrise at Newgrange. Most people will agree that the contexts are such as to virtually eliminate the possibility that what we see today is a coincidence, unintended by the original builders. But most sites are not like this, and when considering a line of two or three standing stones, or even a single stone that does not clearly indicate any direction in particular, we must always put any claim for astronomical observation there to the test of seeing how much of a coincidence is involved. There are several ways of thinking about this, but perhaps the simplest is to say "Suppose I stood here with a pointer smoothly pivoted about its centre. If I spun it, what are the chances that
Freeman: The Statistical Approach
46
it would come to rest pointing in a direction to which I could give some sort of astronomical interpretation?" To answer this, I have to compile a list of all astronomical events that I should find of interest and this can be long, including solar solstices and equinoxes, lunar major and minor standstills, planetary and stellar risings and settings, and so on. The chances of my pointer indicating one of these, to within some limit of error which again I must specify, at any one site, can be quite high. If so, the evidence for astronomical intention at that site alone is weak, but much stronger evidence can be obtained by considering as large a number of sites as possible. If the number showing possible astronomical intention is found to be much greater than the number that would be expected by chance coincidence alone , then a statistically convincing case will have been made. If not, or if no attempt is made even to assess the evidence in this way, then no self-respecting scientist will take the results seriously and the subject of archaeoastronomy will be left even more than it is now to the gullible and the lunatic fringe. As a statistician I have to work with whatever data other people choose to collect. But as Heggie points out, the valid statistical analysis is by far the easiest stage and very few sets of data get through all the previous stages which are needed to qualify them as validly analysable at all. These stages are nearly all to do with subjective biasses and some of them are listed below. The very nature of the subject makes several of them extremely difficult to avoid, or to deal with in ways which most people will regard as fair, but it has to be said that many workers have made far too little attempt to avoid them at all and the credibility of their results has decreased accordingly. I shall now state aphoristically a few very general instructions on how to deal with subjective bias.
RULE 1
OBSERVE EVERYTHING
The choice of what to observe is, I suspect, the biggest single source of bias. We all know that asking a sample of unemployed manual workers for their views on the performance of the current government is likely to give a very misleading idea of the general opinion across the whole country, yet similar elementary mistakes abound throughout the archaeoastronomy literature. It is, I suppose, natural for those people who firmly believe in the astronomical interest of ancient cultures to go and survey those sites which look most likely to support their belief.
When
at a site, it is equally natural for them to only survey those aspects of
Freeman: The Statistical Approach
47
it which fit in with their beliefs, ignoring all other data which they regard as irrelevant but which a dispassionate reader must have in order to assess their work. For example Thorn and Thorn (1981) surveyed a site in Sutherland, consisting of a single menhir about 5 feet wide and 1 foot thick. They surveyed the azimuth of this stone, in so far as it can be said to have one, finding it to be 207°. They then surveyed very accurately the horizon profile for azimuths between 195^° and 199^° only, and after their usual precise calculations conclude that the site was used for observing moonset in a small "notch" at major standstill. This work is, of course, useless as evidence until someone else visits the site and surveys the whole horizon profile so that the "random pointer" concept can be applied. Notice here also how the actual megalithic hardware plays virtually no part in the archaeoastronomical superstructure. In reading the paper one must ask oneself about all the other possible places, unmarked by any megalithic remains, where one might have stood and observed some equally interesting rising or setting. I should like to applaud here the work of the Pontings in recording so carefully complete horizon profiles at Callanish, and I hope to do some statistical work with these in the near future. In this general area it is worth commenting on the various attempts there have been to list criteria for what megalithic remains should be agreed to be potential direction indicators. Thorn (1955) defined a set in his earlier work, but his later (1967) set depends on subjective judgements. Hawkins (1968) said that only man-made markers should qualify, that alignments should be postulated only for a homogeneous group of markers, and that all possible alignments at a site must be considered. Cooke et al.(1977) give a hierarchal list of five classes of alignments, ranging from those along 3 or more stones, through those along only 2 stones down to indications by flat faces of a single menhir. The Thorns' most recent work (1981) has clearly moved far from all these criteria since they state "... the function of the backsight is to mark a position, not a direction." My own attitude is that worthy as these attempts at systematisation are, it is probably impossible to achieve a set of criteria that can be generally agreed and it is not crucial anyway. The really important requirement is that each alignment should be surveyed so as to record not only its azimuth, but the accuracy to which that azimuth can be indicated by the components of the alignments themselves . It is extremely relevant that a pair of standing stones can only
Freeman: The Statistical Approach
48
indicate a direction to within about + \° even when they are slender and spaced well apart, while, for example, the axis of symmetry of a recumbent stone circle or a flat-faced single menhir can get within only + 2° or 3°, and a shapeless single menhir achieves the ultimate + 180°.
RULE 2
REPORT ALL YOU OBSERVE
Some selective judgement certainly has to be made when preparing field work for publication, but any that chooses those observational aspects which support a particular theory in preference to those that do not is obviously misleading. We often see survey plans on which astronomical lines have been superimposed, for example Hawkins (1965) on Stonehenge and Thorn & Thorn (1973) on Brogar. Much time has to be spent thinking about all the other lines which might have been chosen but weren't because they didn't indicate anything interesting. Equally, all workers should report the accuracy to which their measurements were made, and the discrepancies between indicated alignments and theoretical ones. As a statistician I believe in error (indeed, I make my living from it) and am distinctly unimpressed by phrases like "exactly in line with", "spot on". Often a bald statement implying exact indications turns out to cover up discrepancies of several degrees.
RULE 3
STATE CLEARLY THE RELATION BETWEEN HYPOTHESES AND DATA
The whole Popperian philosophy of science, in which a hypothesis is constructed to be consistent with all known data, an experiment is designed to test the hypothesis on new data, is then performed and the data are assessed for consistency or conflict with the hypothesis, is almost totally ignored in archaeoastronomy. This is not only because it is an observational rather than experimental science (so is ordinary astronomy, after all), but because it is much more difficult to adopt this philosophy than to ignore it, and because many workers (including the Thorns) seem to be unable to see any virtue in it at all. The dangers of choosing a hypothesis to test after having inspected a set of data and found something unusual in it are well known. A classical example is the 18th century debate about whether the fixed stars are randomly arranged over the celestial sphere. It was agreed that the existence of the Pleiades was convincing proof of non-randomness, since the probability of finding 6 stars all of magnitude 6 or greater all within 49' of arc of each other under a purely random arrangement is only 1
Freeman: The Statistical Approach
49
in 33,000. The obvious counter-argument is that many purely random arrangements will display some striking feature (3 stars nearly in a row, 4 stars nearly forming a parallelogram, a group reminding you of a pussy cat, etc.) which if then selected and tested for would also have a very small chance of occurrence. It is, I think, possible to push this argument too far, since many important advances in science have come from such fortuitous noticing of striking patterns in data, but all due allowance for them must be made if at all possible. The Thorns have, after all, always reported their surprise on constructing histograms of circle diameters or alignment declinations without ever commenting on what other kinds of histograms they would have found just as surprising. Even more dangerous, of course, is adapting hypotheses from one dataset to another. This new site shows no sign of solar or lunar indication? Never mind, try the planets, some stars, a few different dates, something is bound to work. One can only guess how much of this kind of thinking goes on behind the scenes as it is so easy to cover up in papers. My personal precaution is to hold a hierarchy of plausible targets at the back of my mind, ranging from solar solstices through solar equinoxes, lunar major and minor standstills and the lunar wobble down to stars of decreasing visual magnitudes. The statistical significance of any set of claimed alignments is then assessed using all targets in this list at or above the lowest level of those that are claimed. If allowing data to suggest hypotheses is potentially misleading so also is the converse sin of allowing hypotheses to dictate what data are collected. This leads to beautifully circular arguments, as in the Thorns' work on Avebury (1976) where the existence of a megalithic yard of 2.720 feet and knowledge of Pythagorean triangles is assumed in "reconstructing" the geometry, and a least squares fit is then used to reconfirm a megalithic yard of 2.722 feet. If, on the other hand, a least-squares fit is done without preconceptions (Freeman, 1977) no evidence of either a megalithic unit nor of a Pythagorean triangle is found. The archaeoastronomical equivalent of this is found in the Thorns' work (1971) on Er Grah, where lunar observations are assumed, the directions in which to look for possible backsights are calculated and required stones then located, several of mightily unimpressive size. There are, of course, so many standing stones in the region that the lunar hypothesis when forced upon the site is almost bound to lead to
Freeman: The Statistical Approach
self-fulfilling prophesy
50
(see Atkinson 1975, Freeman 1975).
An example Lest it be thought that all these objections to widespread current practice set standards which it is impossible for any dataset to satisfy, I conclude with one which, though not perfect, is pretty good. This is a set of surveys of 31 recumbent stone circles in Cork and Kerry conducted by Dr Jon Patrick. The sites are archaeologically and culturally homogeneous (I should perhaps emphasise the importance of this, even though it is rather outside the scope of this paper). Although there are probably as many sites again still waiting to be surveyed, there is no reason to believe that the selection of sites has led to astronomical bias. For each site, Patrick has recorded
(a) the azimuth of the axis of symmetry, assuming a consistent use of the direction from portals to recumbent, (b) the inherent accuracy to which that azimuth can be determined (c) the latitude of the site, (d) the horizon altitude in the direction of the indicated line, These form the input data to a computer program by Freeman and Elmore (1978), the output from which forms fig.l. The horizontal axis is the allowable discrepancy a between indicated declination and the "target" ones - here taken to be solar solstices and equinox, rising and setting, upper and lower limbs - while the vertical axis is the value of the test statistic
z. Since on the "random pointer" hypothesis this should have a
standardised Gaussian distribution, with negative values denoting more coincidences than by chance, we need values of preferably below
-3 ,
z
below
-2 ,
and
to provide any evidence of astronomy worth
considering. Here we can see there is no evidence for sun observations at all. The full results from this dataset will, we hope, be published elsewhere. Finally, I am always most interested in hearing from anyone who has similar homogeneous, unbiassed data suitable for statistical analysis.
51
Freeman: The Statistical Approach
degrees
-1
-2
Fig.l.
Statistical analysis of Irish recumbent stone circles.
Freeman: The Statistical Approach
52
References Atkinson, R.J.C. (1975). Megalithic astronomy - a prehistorian1s comments. J.Hist. Astron.,^, 42-52. Cooke, J.A., Few, R.W., Morgan, J.G., & Ruggles, C.L.N. (1977). Indicated declinations at the Callanish megalithic sites. J.Hist. Astron.,j8, 113-33. Freeman, P.R. (1975). Carnac probabilities corrected. J.Hist. Astron.,6^, 219. Freeman, P.R. (1977). Thorn's survey of the Avebury ring. J.Hist. Astron.,£, 134-6. Freeman, P.R. & Elmore, W. (1979). A test for the significance of astronomical alignments. Archaeoastronomy, 1_, S86-S96. Hawkins, G.S. (1965). Stonehenge decoded. London, U.K: Souvenir Press. Hawkins, G.S. (1968). Astro-archaeology. Vistas in astronomy,_l£, 45-88. Heggie, D.C. (1981a). Highlights and problems of megalithic astronomy. Archaeoastronomy 3, S17-S37. Heggie, D.C. (1981b). Megalithic Science, London, U.K: Thames and Hudson. Thorn, A. (1955). A statistical examination of the megalithic sites in Britain. J.Roy. Statist .Soc .A, lJJJ, 275-295. Thorn, A. (1967). Megalithic sites in Britain. Oxford, U.K: Clarendon Press. Thorn, A. & Thorn, A.S. (1971), The astronomical significance of the large Carnac menhirs, J.Hist. Astron. ,2., 147-60. Thorn, A. & Thorn, A.S. (1973). A megalithic lunar observatory in Orkney: the ring of Brogar and its cairns. J.Hist. Astron. ,4-, 111-23. Thorn, A., Thorn, A.S. & Foord, T.R. (1976). Avebury (1): a new assessment of the geometry and metrology of the ring. J.Hist. Astron.,^7, 183-92. Thorn, A. & Thorn, A.S. (1981). A lunar site in Sutherland. Archaeoastronomy 3, S71-S73.
53
STATISTICAL AND PHILOSOPHICAL ARGUMENTS FOR THE ASTRONOMICAL SIGNIFICANCE OF STANDING STONES WITH A SECTION ON THE SOUR CALENDAR
A. Thorn Thalassa, The Hill, Dunlop, Kilmarnock, KA3 4DH. A.S. Thorn, The Hill, Dunlop, Kilmarnock, KA3 4DH.
Abstract. Stressing the importance of the lunar bands, the authors show that within each of these bands, the histograms of declination give strong support to the lunar hypothesis, because of the clustering of the alignments round the expected values. Recently, while considering which lunar band edges would be favourable or unfavourable for the erectors, the authors have discovered a way of presenting the data published up to 1978. This Favourable/Unfavourable objective consideration gives strong support to the hypothesis, since nothing was known of it over the decades when the surveys were made. The method shows a low probability (l in 433) that the lunar alignments are occurring by chance alone. By reasoning from the viewpoint of the erectors, the authors give several supporting philosophical arguments which by their very nature can not be used statistically; e.g. the warning positions which could well have been occupied by an assistant observer to tell the row of observers at the backsight of the imminent Moonrise. A revised histogram of solar lines is presented with the 16-month calendar based on a 365/366 day year. It is suggested that the erectors had two reasons for recording the Moon's movement; (a) eclipse prediction assisted by their solar calendar and (b) scientific curiosity.
1
INTRODUCTION Our knowledge of megaliths can come only from the remains them-
selves.
These consist of standing stones, their positions relative to one
another, to tumuli, to mounds, and to nearby tracks on the ground. addition some of the stones have cup and ring markings.
In
It is generally
accepted that some of the standing stones are arranged to indicate the rising/setting points of the solstitial Sun, but why stop with the solstices, and why not consider the Moon as well?
The types of foresight
used at various places are detailed in Thorn & Thorn (1980 b ) .
Accurate surveying for declination. make accurate surveys of the stones.
To take the subject further we must Standing at the backsight, i.e. at
or near a standing stone, we measure by theodolite the altitude and azimuth
Thorn & Thorn: Astronomical significance of standing stones
of the foresight.
54
For the azimuth, observation of the Sun is necessary,
using an accurate watch.
Knowing the latitude of the backsight we can then
determine the required azimuth by spherical trigonometry.
From the measured
altitude and azimuth, again using spherical trigonometry, and our knowledge of refraction, we calculate the declination of the foresight and so we know, to within a minute of arc, the declination of any heavenly body that rose or set on the foresight.
We then examine the declinations thus obtained.
If the standing stones have nothing whatever to do with astronomy then the declination will be spread at random throughout the range.
If on the
other hand the declinations fall into clumps around significant points then we know that we are dealing with stones erected for astronomical use. to 1967 we had observed about 260 declinations. Fig. 1 which is taken from Thorn (1967). group around germane declinations.
Up
These are shown plotted in
It is evident that the points
Our critics say that we perhaps
unintentionally use subjective methods in selecting our foresights but we can not have done this every time.
We consider that our choice was not
subjective, and this is where the matter rests at present.
V/e have several
times stated that megalithic man was able to detect the small nine-minute perturbation A
of the lunar orbit.
This needs much more careful consider-
ation and in our analysis we must use much more sophisticated methods.
2
STATISTICAL VIEWPOINT In our long investigation into the astronomy of Megalithic Man
the greatest difficulty all along has been to decide just when a line should be neglected.
On the one side people are asking for evidence, on the other,
statisticians are waiting to point out any irregularities. objective criteria.
We try to use
No matter what terms of reference are decided at the
beginning,however, there are always borderline cases. an answer to the question:
We want to produce
Did Megalithic Man really use advanced astron-
omical methods for calendrical purposes, for eclipse prediction, or had he perhaps purely scientific reasons?
We wish to find the answer in a form
that will be acceptable to archaeologists but we find much greater difficulty in satisfying statisticians who wish to apply rigid statistical methods thus excluding any philosophical approach. When in 1955 the senior author gave his first paper to the Royal Statistical Society (Thorn (1955)) the atmosphere was quite different. For example, when he asked an eminent statistician how to obtain a proof of a certain idea of his, the answer was:
"It does not require proof.
It
Thorn & Thorn: Astronomical significance of standing stones
is obvious".
3
55
That particular idea has since been attacked several times.
LUNAR OBSERVATIONS Let us look at one of the lunar sites, that at Brogar in Orkney,
Thorn & Thorn (1978 a) Chapter 10.
Like many other backsights, it occupies
a relatively flat area over which the observers could move to fix exact
Fig. 1.
Histogram of observed declinations, Thorn (1967)
1 4 r i
o
Thorn & Thorn; Astronomical significance of standing stones
positions from which finally to observe phenomena on the horizon. itself stands on top of a gentle rise.
56
The ring
It was built perhaps early in the
third millennium. At that time the rising Moon as seen from somewhere within the circle at the minor standstill rose on the notch at Mid Hill and when setting ran down the edge of the impressive cliffs at Hoy. passed the obliquity of the ecliptic £
As the centuries
fell and it was necessary to move
the sighting points outside of the south of the circle if the two foresights were to be retained.
Also by this time the standard of observing
was very much higher. The casual visitor misses a great deal at this site.
It should
be noted how the old track passing through the low mound at the Comet Stone, Thorn & Thorn (1978 a ) , Fig. 10.7, points exactly to Mid Hill. should be examined in profile (from below). practically ploughed out today.
Mound L 2
It will be seen that it is
At T, most of the traces of a mound shown
on Thomas's map have been removed to enable visitors to walk round the outer ring without stumbling on loose stones. Warning positions.
It must have been necessary to have warning that the
Moon was about to appear so that the observers at the Comet Stone would be ready.
The notch on Mid Hill where the Moon rose is on a long ridge
sloping down to the east.
A little thought shows that the best stance for.
a warner was some way to the east, but this was not possible because of the presence of the loch and so he had to be raised and this fully explains the presence of mound A.
AB points to Mid Hill and so there would probably have
been a marker on mound B so that the warner would know where he himself should watch.
We consider that the presence of mound A is a good
philosophical proof of the lunar hypothesis.
Its position and height are
so perfectly explained. On our plan of the site we give numerous spot levels which show that the line MLJ is on a ridge.
Advantage was taken of this ridge to
place the row of mounds pointing to Mid Hill.
The position for observing
Mid Hill was obviously at the base of cairn M.
Cairn M itself was raised
to provide a stance for a warner for the man below. cairn M was large and dilapidated.
Thomas reported that
It was also necessary to place the
warner to the north west of the site so that he could say when the Moon was going to appear at Kame of Corrigal;
but movement to the north meant
losing height slightly and so Salt Knowe was raised at the position to suit.
The foresights at Ravie Hill and the cliffs at Hellia do not need
any warning position as they are for the setting Moon.
Thorn & Thorn: Astronomical significance of standing stones
57
The foresight for the Moon rising at Mid Glyth (Thorn (I97l)p9l) is very small.
It needed a warning position.
There is a row of large
boulders on the moor above Mid Clyth pointing to the notch and this was the position to be occupied by the warner, see above.
At Kintraw (Thorn (l97l)
p39) there is a stone above, obviously placed for a warner to let the observers at the Susan Stone know that the Sun was coming.
It is highly
probable that at many sites a row of observers stood in line and watched as the phenomenon occurred.
The position occupied by the first (or last)
to see the limb was the required point on that day. Arguments like the above seem to us to be very important. They cannot contribute anything to, for example, the probability level, but without them the probability level is bare and uninteresting.
The
various points made above must be used in a philosophical manner to lend support to the astronomical argument.
4
LUNAR BANDS To return to our present day analysis of the problem,we need
only consider those sites which give declinations falling inside the lunar bands defined by the limits + £ + (i + A + s) and + £ +(i -£> - s ) , where € is the obliquity of the ecliptic, i is the inclination of the Moon fs orbit to the ecliptic, A
is "the perturbation of the orbit and s is the
semi-diameter of the Moon. A lunar band for £ + i is shown diagrammatically in Fig. 2.
Relevant numerical values are given in Table 1.
Eight lunar
bands exist on the horizon, four for rising and four for setting Moons.
Fig. 2. Lunar band, showing the limiting positions of the upper and lower limbs of the rising Moon at standstill. Appropriate numerical values of /i and s are shown for equinox and solstice.
Band
Thorn & Thorn: Astronomical significance of standing stones
58
From the declinations falling within the lunar bands we deduct ( € * i)»
If there is no astronomical significance in the foresights then
there is no reason why the histogram of the points so obtained should not smear out over the lunar band widths of 2(s + A
) , about 50 f «0.
The fact
is however that they do not smear out but pile into little clumps, see Fig. 4, adapted from Thorn & Thorn (1980 a) Fig. 2. have been overlooked by many of our critics.
This argument seems to
We may have included a few
spurious lines but these can not affect the main argument, more especially when this is reinforced by the philosophical points mentioned above.
4.1
Four histograms of /3 values Our surveying has supplied us with declinations
which rise or set on the foresights.
i o of bodies
From these observed declinations
oo
we deducted ( € i i ) . Calling each difference /3 , where fi - oo - ( 6 - i ) , we proceeded to compare each J3 with Q, the "expected value". the values of ± ( A ±
s
).
Q, has one of
Fig. 4 shows histograms of the values we
obtained for/3 •
Equinoxes.
Above the four histograms we have marked with wide-shafted
arrows the theoretical or expected values of Q, at the equinoxes.
These are
obtained from Fig. 3 (see Thorn & Thorn (1980 a ) , Fig. l)which shows how Q varies with condition, major or minor standstill, and positive or negative declination.
The manner in which the A
values cluster round the expected,
or Q,, values shows that Megalithic Man was observing the declination maximum M and minimum M_ shown in Fig. 3»
Table 1
+(€ + i + A) +(€ + i + /\4- s) +(e + i + A- s) +(€ 4- i -A) +(€ + i -A+ s) i -A- 3 ) i +A) i +A+ s) i +Ai -A) i -4+ s) i -A- s)
£
Numerical Values of Nominal Declinations
8:6 8.6 8.6 10.0 10.0 10.0 10.0 10.0 10.0
8.6 8.6 8.6
i
S 15 w 15.^ 15.^ 15.6 15.6 15.6 15.6 15.6 15.6 15.^ 15 A
23°53'.1 ;
29° 10:^ 29 28 28 29 28
25.8 55.0 51.8 07 A 36.2
s) - U + i + A - s) -(*+ i - £ ) -(6 + i - £ + s) k - s)
18 !?±A 19 10.0 18 18 18 18 i
38.8
35.8 51.2 20.4
- 5°08'.7
-(*-(* -U -(£ -
.) i +A- s) i -A) i -A+ s) i -A- s)
O
-29° -29 -28 -28 -29 -28 -18
109A 25.8 55.O 51.8 07.4 36.2 54.4
-19 -18 -18 -18 -18
10.0 38.8 35.8 51.2 20.4
Thorn & Thorn: Fig, 3.
Astronomical significance of standing stones
Conditions at the standstills.
59
Thorn & Thorn: Astronomical significance of standing stones
Fig. 4« Four histograms of {£ values, where the expected values of /$ , namely Q, are shown by arrows as in the key; Q has one of the appropriate values of ± ( A ± s ) .
INVJ
-nusa/VVJ.9 cip*a 0
O
*& i
CM
In yUrM>-r-lrHrHiHrH-j-
ONON ON ON ON ON ON CNJ : • > CNJ CNJ CNi CN2 CNl I I I I I I I
$ CNrh IN-rHNOvO 0 0 NO H CM O CNJ rH CNi CN1 O 0 WO w
o
to •H U
I
o o x: •H EH
o o C t co i cr3 «H ci >H o •
64
Table 2 continued Name Camus an Stacca it
ii
ii
Fowlis Wester N
Escart Crois Mhic-Aoidha t«
II
Parc-y-Meirw Haggstone Moor M
II
Kintraw it
Brogar-Hellia Brogar-Mid Hill Brogar-Mid Hill Dirlot Lund,Shetland Lundin Links
Site A6/1 A6/1 PI/10 PI/10 PI/10 A4/l AV9 V9 W9/7 G3/2 G3/2 A2/5 A2/5 03/1 01/1 03/1 Nl/17 Zl/1
Nominal -28° 55JO -28 37.8 +29 25.8 +29 25.8 +28 36.2 -28 39-3 -28 36.2 -28 37.3 -28 36.2 +18 18.0 +18 20.4 +18 19.7 +18 20.4 +19 09.9 +19 10.0 +18 17.8 +18 20.4 -18 20.3 -18 20.4 -18 4-0.6 -18 38.8 -18 51.2 -18 50 -18 51.2 -18 50 -18 19.5 -18 20.4 +19 10.0 11 -18 17 -18 20.4
rt/i
-18
Table 3
Hl/5 28°35!4 Nl/7 Nl/14 A4/9
-28 37.3
Nl/17 Z3/4 A6/1 28 39 A4/17 29 04.6 H3/11
Observed
Reference MLO Table 7.2 etc.(Thom(197l))
-28° 58-28 39
18
-18
n
II
11
MLO p.54 MRBB Jlg.13.5
11
H
(Thorn & Thorn (1978 a))
MLO Table 5-3 (Thorn (1971)) MLO Table 7.1 MLO Table 7.1
MRBB Table 10.1 (Thom & Thorn(1978 a ) ) MLO p . 9 7 MRBB p . 163 MLO F i g . 5 . 5
20.4
(Thorn (1971)) (Thom & Thom(1978 a ) ) (Thom (1971))
L i s t of 15 U l i n e s
Callanish V Loch of Yarrows Camster Crois Mhic Aiodha Dirlot Wormadale Hill Camus an Stacca Carrach an Tarbert Leacach an Tigh Cloiche to Wiay
Class 3 3 3 3 3 3 3 3 1
U U U U U U U U U
N3/l A4/1 G3/2 Pi/10 A2/5
29°08!7 28 39.3
Mid Clyth Escart Long Tom Haggstone Moor Brogar to Ravie Fowlis Wester Kintraw
Class 1 2
U U
2 1 1 2
U U U U
Thorn & Thorn: Astronomical significance of standing stones
66
Class 3 lines, both favourable and unfavourable, we are left with a total of 33$ made up of 26 favourable plus 7 unfavourable, and we obtain a probability of 1 in 1500.
Thus we get an improvement in probability level
when we remove the 8 weak lines and all of the 10 other remaining Class 3 lines. It is clear that in our selection of lines as described above we did not have anything like the P/U method in mind when we surveyed the sites on which it is based and so no subjective bias was possible.
It thus
appears that the P/U method gives definite support to the lunar hypothesis.
6
SOUR OBSERVATION:
THE CALENDAR
When we look at our collection of declinations in Fig, 1 taken from Thorn (1967)9 Pig, 8.1, we see that some are lunar and a number are perhaps stellar but in addition definite clumps exist near 0 , ^ 8 , **• 16 , i 22° and * 24 . that near 0
The large clumps near ± 24
is equinoctial.
are obviously solstitial and
It will be shown that many of the others are
also for the Sun at dates which divide the year into 16 parts that we might call "Megalithic months".
The length of the tropical year in 1800 B.C. was
365.2424 days but for the present purpose this will be approximated to j6%days.
6.1
The megalithic calendar in Britain We have shown already that Megalithic Man made sophisticated
observations of the Moon.
For this he must have had a calendar.
suitable calendar has been described in Thorn (1967) Chap. 9» believe that this was used.
an(
A w
i ©
Curiously, while many attacks have been made
on our lunar hypothesis, the calendar has been almost ignored.
We do not
know whether this is because it is so obvious or because it appears so complicated that it is not understood.
Here it is proposed to give the
evidence existing today. It must be emphasised that the declinations we have used were mostly measured before we knew about the calendar and it was from these that we deduced the calendar explained here.
It had of course been
pointed out previously by Lockyer (1906) that the May Day/Lammas and the Candlemas/Michaelmas lines at * 16
existed.
Megalithic Man could count and if he observed that the Sun rose on a well-defined mark on a spring morning he would find that 365 days later it rose nearly on the same mark.
After a few years he would however
Thorn & Thorn: Aateonomical J3lgnlfi£anc.&. of standing a toJtea
61
see that the rising point (assuming he continued to uae exactly 365 days to a year) was moving slightly to the right each year.
Matters could only
be corrected if he inserted an extra day every fourth year.
Megalithic Man
was certainly not inferior to modern man in intellectual ability and we can only explain what we find by assuming that he used his ability to think and constructed a calendar based on a 365/366 day year.
With every fourth
year a leap yearf his year would be 365i days long. Fig. ^ shows a histogram of observed megalithic declinations from - 25° to + 25°. Those taken from Thorn (1967), Table 8.1 are listed here in Table 4«
35 lines not in Thorn (1967) and those more recently
surveyed are given in Table 5»
In Tables 4 and 5 Class A refers to those
lines which have, at the backsight, some indication of the foresight;
in
Class B, indication is poor or absent. We divided the year into 16 parts (megalithic months) and calculated the declination at the beginning of each month.
For the rising
and setting cases in the histogram, Fig. 5» the declinations are shown above and below the line respectively.
It will be seen that every one of
the theoretically calculated values carries a group of observed declinations. Broadly this is the case for the megalithic calendar.
6.2
Theoretical declinations With 1/16 of a year for the length of a month, that is 22,
23 or 24 days, the greatest difficulty is to know which length to allot to each of the various months.
Any symmetry which our modern Julian
calendar originally had was ruined when Augustus, jealous of Julius Caesar, left February with 28 days. We shall call the beginning of each month the epoch.
For the
present purpose let us assume that the year began at sunrise on the day of a vernal equinox (zero epoch).
On this morning the erector then set
up a backsight with a foresight for the rising Sun.
Half a year later
the Sun would rise in the autumn almost on the same foresight, but 365 does not divide into two equal whole numbers. and 183, or I83 and 182 days.
We can divide it into 182
In Thorn (I965), para 4.2, we used 182 for
the first half year, and months of 22 and 23 days. Scheme A.
This we shall call
In Thorn (I967), Table 9.1, we used I83 for the first half of
the year but we allowed one of the months to have 24 days. Here we start with 182 days for the first half of the year (Scheme A ) , but retain 22 or 23 and do not anywhere use 24 days.
68 Table 4 List of observed lines (from M.S.B.,Table 8.1) Glass A - Definitely indicated line Glass B - Poorer indications Site Al/2 Al/4 A2/5 A2/5 A2/12 A2/l4 A4/4 A4/4 A6/1 A6/2 A6/5 A8/1 A9/7 A9/7 A10/2 A10/3 All/2 Bl/8
Glass
Loch Nell Loch Seil Kintraw
A A A
ii
B
Duncracraig Dunamuck So Ballochroy it
Camus an Stacca Strone,Jura Tarbert,Jura Mid Sannox Stravannan Bay ti
II
A B A A B B B A A A A
Lachlan Bay B Ballimore A BlanefieId Sheldon of Bourtie' A A Bl/18 Ardlair B Bl/26 Loanhead A Bl/26 A B2/4 Esslie (S) 11 A B2/4 (s) A B2/5 Esslie (N) B B3/3 Raedykes A B7/1 Clava B7/10 Easter Delfour A A Dl/7 Barbrook B Dl/7 B G3/3 Laggangarn B G3/3 •t B G3/3 B G3/3 A G3/12 Drumtroddan B G3/13 Wren'sEgg B G3/17 Whithorn B G4/1 Garsphairn B G4/2 The Thieves A G4/12 Cambret B G4/12 •t B G4/12 A Ok/Ik Cauldside B Qk/lk II
it
II
•i
II
It
Ok/Ik
G6/2 G7/4 G8/8 G8/9 G8/9
B B A
Auldgirth Loupin Stanes Dere Street IV B Eleven Shearers A it
if
A
h
1*7.5
146.8 223.9 307.5 140.7 138.2 315.5 226
—C±,O
6.9 0.5 2.7 2.3
-21.3 -23.6 +21.9 -23.7 -21.7 +24.2 -23.6 -24.2 +21.6 - 8.1 -I6.3 -21.7 +22.1 +24.2 -20.6 +24.0
3.4 0.9
-0.1
213.7 4.2 298.3 7.5 106.7 1.5 229.3 6.2 136.O 2.7 3H.5 0.7 4-3.0 0.6 228.2 1.8 56.7 +7.2
119.7 -0.2 116.0 +1.1 41.6 +0.7 139.O 0 . 2 4-3.1 1 . 1 306.2 0 . 2 223.1 2.7 314.2 2 . 1 216.5 1.7 219
284.8 118.6 296
2.0 2.3 2.2 2.1
106.2 0.7 105.4 0.7 133.8 0 . 2 43.3 0.4 227.5 -0.2 254.3 +0.9 100.4 3.2 228 -0.4 296.7 0 . 2 116.7 5.7 254.3 156.8 8.7
59.5
78.2 281.2 306.5 276.7 94.2 109.2
Decl
6'.6
0.3 0.3
3.3 5.1 2.3 4.1 3.1
Az .- Azimuth h - Horizon altitude Remarks
-16.0 -13.4 +24.0 -24.3 +24.1 +18.4 -21.2 +23.9 -24.3 -23.6 +10.5 -15.1 +16.2 - 9.0 - 8.5 -23.7 +24.8 -23.6
- 8.5 - 3.5
-23.4 +14.7 -10.3
- 5.4
-23.9 +16.8 + 6.6 + 8.9 +24.1 + 5.4 + 0.8 Exact azimuth uncertain - 8.3
69
Table 4 continued Site G9/13 Hl/1 Hl/1 Hl/1 Hl/3 Hl/3 Hl/4 Hl/4 HI/7 HI/7 HI/7 HI/10 HI/14 HI/15 H2/1 H2/2 H3/1 H3/2 H3/6 H3/8 H3/8 H3/9 H3/18 H3/18 H4/4
H5/1 H6/3 Ll/1 Ll/1 Ll/1 Ll/3 Ll/6 Ll/6
L./6 Ll/6 LI/7 LI/7 M2/6 M2/9 M2/10 M2/14 M2/14 M2/14 M2/l4 N2/1 N2/1 N2/1 N2/1 Pl/1 Pl/1
Class A A A
Kell Bum Gallanish I ti
ii
II
M
III II
II
IV II
II
Gt Bernera II
Steinacleit Clach Stein Dursainean Glach an Teampuill Clach Mhic Leoid Glach Maolrithe Clach ant Sagairt Barpanan Feannag Na Fir Bhreige it
M
M
Ben a Gharra Sornach Coir Fhinn it
II
it
Rueval stone An Carra Brevig, Barra Castle Rig M II
•i
II
Sunkenkirk Burnmoor D to G 11 D to E
Burnmoor C to D G to E Long Meg M
II
Ross of Mull Ardlanish Uisken Loch Buie II
II
M
II
II
II
Learable Hill ti II
II
Muthill II
it
A z
o
309.8 270.9 77.8
B B B B B B B B B B A B
142 280 249 89 135 236 83 90
A A A
271.0 296.6 287.5 220.0 288.9 271.8 255.7 303.2 318.5 303.8 315.4 135.0 251.5 127.0 307.0 128.8 243.6 131.9
B B A B A A A B A A A A A B
B
B B A A A B B A A A B A A A B A A
89.I 98.3 227.9 138
63.6 112.3 223.4 65.1 59.9 282.4 229.6 123.4 223.6 237.0 150.8 92.8 61.6 75.0 92.8
57.3
237.3
h
2f.9 0.5 0.9 0.5 0.6 1.7 1.0 1.4 1.7 0.7 0.7 0.4 2.0 1.9
-0.1 -0.2 0.0 0.6 2.3 0.4
-0.3 0.6 0.8
-0.1 -0.1 -0.3 3.2 5-2 4.6 0.5
-0.5 +1.6
4.3 2.6 1.1 3.4 1.5 2.6 0.3 6.8 0.4 2.1
5.1 2.4 2.4 2.2 2.4 1.8
5.6
Decl +23?5 + 0.3 + 6.9 -24.5 + 5.4 -10.2 + 1.0 -22.8
Remarks
-16
+ 6.0 + 0.2 + 0.7 -4.5 -19.3 -21.8 0.0
+13.2 + 8.8 -24.2 +11.7 + 0.8 - 8.1 +21.6 +24.0 +I6.9 +21.9 -23.6 - 8.1 -16.0 +24.3 -21.5 -16.0 -21.7 Adjusted to suit average of several surveys,Az to * 6 f ; 1 h to i 2 . +18.5 -10.8 -24.2 +16.7 +17.1 + 9.0 -21.3 -12.0 -23.7 -16.0 -24.2 + 0.3 +16.6 + 9.5 + 0.4 +18.7 -12.7
70 Table 4 continued
Site Pl/19 P2/12 S2/2 S6/1
Groftmoraig Dunkeld Merrivale Rollright Penmaen-Mawr
W2/1 W2/1
it
Class B
ii
W5/2 W6/2 W6/2 W8/1 W8/l
Twyfos Rhos y Beddau
W9/2 W9/2
Gors Fawr
Wll/2 Wll/2 Wll/2
Y Pigwn
Wll/4 Wll/4 wi]/4 Wll/4 W8/3
Usk River
••
ii
Rhosygelynnen ti
II
II
II
II
H
•i
H
II
M
II
H
II
II
Four Stones
B A A A A A A B A A A A B B B B B A A B
h 101°. 7 310
8'.9
3.7
70.4 3.5 95.0 -0.2 60.9 -0.2 240.9 +3.7 118.6 5.0 79.1 5.0 259.1 3.8 82.0 0.6 262.0 2 . 2
49.6
1.3
53.3 233.3
0.4 1.0 0.9
229.6 -0.2
Degl + 0.8 +24 +14.9
Remarks
-3.8 +16.4 -14.1 -12.7 +10.4
- 3.7
5.0 - JA
Az of short line uncertain
+24.3 -24.2 +21.5 -21.0
131.0 285.O 78
1.5 3.3
+10.1
295.3 115.3 67.5
1.2 2-9 0.9
+16.0 -13.1 +13.9
-23-5
+ 9.7
Megalithic Man divided the year into 16 nearly equal parts, as today it is divided into 12 nearly equal parts.
The 16-month year is not superior
to the 12-month, for in neither system can the months be of equal length.
6.3
The orbit of the earth The earth describes an elliptical orbit about the Sun, and so
the Sun appears to move around the earth in an ellipse.
Particulars for
1800 B.C. are:- £ = obliquity of the ecliptic = 23°.9O6, 7T= longitude of the Sun at perigee = 218°.067 and 6 = eccentricity of the ellipse = 0|.0181. Aries.
Longitude is measured along the ecliptic from the first point of Let us put(£)= longitude of the Sun and X = longitude of the
dynamic mean Sun, that is a Sun which moves uniformly.
©
Knowing £, we get
from
O s i + 2 e 5in(i -7TJ
Eq. 1.
Since )(, advances uniformly with time we put the constant of proportionality D = 360/365-^ degrees per day and so we can write
Dt
Eq. 2.
Table 5 Additional observed lines, surveyed since 1967 Az0 Site Glass Map Ref. 127.8 B NR 863946 A2/15 Torbhlarum A2/16 Nr Kilmichael 71.8 7.8 Glassary (Moor) B NR 855950 B or 63.3 8.0 254.4 11.2 A2/23 Craigantairbh B NR 862016 86.4 3.0 A2/18 River Add (Moor) B NR_933981 A2/22 Ford (S) B 56°10 5°26< 215.5 5.7 217.3 5.9 A4/16 Culinglongart B NR 652120 B NT 617777 256.5 G9/7 East Linton (E) B NF 770661 H3/12 Glach Mor a Che 281.9 0.4 A NG 420490 H7/4 Glach Ard 110.5 1.2 B H7/4 46.1 2.7 6°3O' 118.1 3.2 H8/2 Pounding StonefCanna B 57 B H8/2 288.1 0.6 B 57C H8/4 Gramisdale Canna 6°36< 65.5 0.3 B H8/4 245.3 1.4 B NY 592129 12/13 Oddendale 252.0 1.7 A ND 126208 Nl/20 Cnoc na Maranaith 320.3 ^4.5 B NC 582049 N2/3 Shin River A to B 147.5 4 A NO 156272 P2/8 Shianbank A to B 317.5 0.6
P2/8 •• B to A B3/3 Raedykes A to B PI/14 Tullybeagles A to B
PI/14 " B to A Wll/2 Trecastle B to A Wll/l4Usk River £ to W Pi/10 Fowlis Wester W to E Pi/10 " " E to W PI/10 " P2/17 Dowally
B NO 832907 B NO 010361 B B SN 833310 B SN 820258 A NN 924250 A NN 924250 B NN Q 924250 B
3°37:8' P2/17 P4/1 Lundin Links W9/3 Cwm Garw Zl/1 Lund
B B 403027 B SN 119310 A HY 578034 A A
137.5 2.6 314.2 2.1 84 0.1 264 3.8 53.3 0.1 295.3 1.2 88.5 -0.1 268.5 1.8 299.3 2°50'
Decl
Remarks "Fort" 128
+16.4 +21.2 + 0.8 + 3.8 -21.8 -21.6 - 6.8 + 6.2 -10.2 +24.1 -12.4 + 9.8 +12.8 -12.3 - 9.1 +24.1 -23 +24.5 -21.9 +23.9 + 2.9 - 0.3 +21.3 +16.0 + 0.5 + 0.3 +18.7
288 +13.7 108 - 4.0 234 0°20' -19.2 5.2 - 6.8 259.^ 218.6 3°42( -I8.3 154.2 2°18' -24.2 47' +24.1 324.0
Shaky stone. Pimple Compass only. Pimple Long stone.Broken off Stump 71°•5 8f stone orientated 86/92 Two on old 6" O.S. map 10• stone orientated 220 10' stone 257 Point to be used on foresight ig unce: Sculptured stone orientated 110 The notch is a good foresight Orientated 115 or 29O Reverse Stone 1 x 0.5 x 3.5 ft Reverse Double circle. Outliers MRBB pl71 (Thorn & Thorn (1978 a)) MRBB Table 3.7 (Thorn & Thorn (1978 a)) Two rings. MRBB Table 3.7 (Thorn & Thorn (1978 a)) MRBB Table 3.7. Ruinous " " " Pair of circles. MRBB Table 3.7 (Thorn
0 ^ 0 v
0
-'
0
0
°
•
^0
,.| w
0 0
„'
0
^> o
o° °
HOLtS
°
Q
o Q
o
HOI tS
X\
1C
v? . '">
• •
-
•
0
40
80
.
!
.
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